i did some mental math, but hit a wall at trying to find the square root of 63,252,753,001

@iamgroot3615

5 жыл бұрын

that’s some impressive mental math assuming you’re telling the truth . Is there a trick or something

@AngryAxew

5 жыл бұрын

@@iamgroot3615 theres no trick hes probably lying

@AngryAxew

5 жыл бұрын

r/iamverysmart

@marvinfung2050

5 жыл бұрын

AngryAxew there's no reason not to be able to mental math those numbers Like 500(500+1) which is easier which is 250000+500 and it similar to the end

@narayanankannan6787

5 жыл бұрын

I mean it's OBVIOUSLY 251501.

Wow... this essentially proved that if you take the product of four consecutive -numbers- integers and add one to it, than it's gone be a square number.

@ClimateAdam

5 жыл бұрын

Awesome! Good spot!

@fanyfan7466

5 жыл бұрын

Gábor Tóth holy shit you’re right! That’s crazy man

@blackpenredpen

5 жыл бұрын

Yup!!

@kingbeauregard

5 жыл бұрын

The most pathological case I can think of is -1 thru 2, and yes indeed I get 1, which is a perfect square.

@pcklop

5 жыл бұрын

My professor had us prove a more general result: take the product of four numbers in arithmetic sequence, then add the fourth power of their common difference. Show that the result is a perfect square.

1990: we'll have flying cars by 2019 2019: 2=1+1, wow I'm a genius

@blackpenredpen

5 жыл бұрын

LOL

@ghotifish1838

3 жыл бұрын

2+2 is 4, minus one that's three quick maths

@Kyanzes

3 жыл бұрын

Flying cars... you can't even have a sharpie that could change color. Say, red and black.

@santinodemaria2818

3 жыл бұрын

@@ghotifish1838 topical meme reference

@unutentediyoutube3282

3 жыл бұрын

Well it can also be 2=500-498

I just started learning English, but the explanations are clear and interesting even at my levels of English. Thanks a lot 😁👍

@blackpenredpen

5 жыл бұрын

Юлия Охременко I am Glad to hear!

@enhace15anos.83

4 жыл бұрын

x2

@corona8073

4 жыл бұрын

U r indian Chinese korean or ....???

@donovanholm

4 жыл бұрын

@@harelavv8806 the name may seem obviously Russian to some but not all

@siddharthsoni2101

3 жыл бұрын

@@blackpenredpen hii

Olympic math taught me that insanely hard problems often had elegant solutions, this is no exception.

@blackpenredpen

5 жыл бұрын

: ))))

@hafizh8461

4 жыл бұрын

@@leif1075???

@hemandy94

4 жыл бұрын

@@leif1075 people like these are called problem solvers...

@drudi1

4 жыл бұрын

@@leif1075 well it took me about 5min to solve it so I think is not impossible to solve. All of this types of equations where you have 4 consecutive numbers multipled are done like this

@jayasri6764

4 жыл бұрын

Lol,This problem is actually super easy,(Every single Olympiad contestant would have solved this question,at some point of their life) .Insanely hard problems need not have simple solutions . That's a downside of the math Olympiad .They make you expect difficult problems have simple solutions.(Although,most imo contestants don t fall for this fallacy).Real insanely hard problems have not been solved by anyone,yet.

My last words whispered in a final breath : "Don't forget the +1"

@not_So_Random-Dude

3 жыл бұрын

😂

@68plus1.

2 жыл бұрын

LMFAOOO

@naiknaik8812

2 жыл бұрын

He never resumed the video

@user-tk4dj4il5s

10 күн бұрын

He added the one wdym 🧐

Instead distributing at 4:18 u = x^2 + 3x + 1 (u - 1)(u + 1) + 1 = u^2 So the root is x^2 + 3x + 1 = 251501

@blackpenredpen

5 жыл бұрын

Bryan Lu omg that cat!!!!

@AmitBentabou

5 жыл бұрын

Or even u=x^2+3x, then u^2+2u+1

@matias12381

5 жыл бұрын

digno de nyan cat, jajajajaj

@mattat3847

5 жыл бұрын

My life is a lie. I thought u subbing was only for integrals

@RunstarHomer

5 жыл бұрын

@@mattat3847 nah man, sub whenever it makes the problem simpler

i put it in my calculator and got 251501, that was easy

@bowtangey6830

4 жыл бұрын

Boo!

@Netherexio

3 жыл бұрын

@The Balton American calculators are beasts

@paradox9265

3 жыл бұрын

@@Netherexio Agreed but Americans aren’t

@Netherexio

3 жыл бұрын

@@paradox9265 What do you mean?

@user-yp6eb5wj4w

3 жыл бұрын

It was easy, but not so beautiful like this)

Did you know that 2 = 1 + 1?? I bet not! jk : )

@williamadams137

5 жыл бұрын

blackpenredpen No i don’t, i need a calculator to this

@snejpu2508

5 жыл бұрын

That's pretty funnt, but sometimes such things are the most difficult to see, for example: we have f(x)=x^4+8x^3+18x^2+8x+17, and a question, for which x, the function f(x) is a prime. You can check infinitely many cases and never know the answer, but what makes this question easy (but on the other hand is not so obvious), is that 18=17+1. Because then we have (x^2+1)(x^2+8x+17), which has to be a prime. One of them has to be = 1, the other one has to be some prime then... We are left with only 2 cases, because we know, that 18=17+1. : )

@theolbiterator5408

5 жыл бұрын

No but I knew 2= 0.9+1.1.

@chaitanyagadekar5025

5 жыл бұрын

I Known 2+2 = 5

@clubstepdj

5 жыл бұрын

What i know is 5/2 = 2 with int data type

"If you're using a calculator, why are you watching this video?" Sanity check.

@blackpenredpen

5 жыл бұрын

hahahahaa

@andrel8243

3 жыл бұрын

I am a calculator, not a person

@mysticdragonex815

2 жыл бұрын

*laughs in Shakuntala Devi

Jeez thats smart *proceeds to use the calculator to prove that 251501 is the right answer*

Dafuq did i jusf watch.i lost it when the 2=1+1

@executorarktanis2323

4 жыл бұрын

You are not nerdy enough

no 2=1+1/2+1/4+1/8+1/16... you have got many misconceptions blackpenredpen!!!

@iabervon

5 жыл бұрын

When he writes 1, he's obviously just abbreviating 1/2+1/4+1/8+1/16+...

@InDstructR

5 жыл бұрын

@@iabervon and when he writes 1/2 he's abbreviating for 1/4+1/8+1/16+...

@agces2001

5 жыл бұрын

@@InDstructR And when he writes 1/4 he's abbreviating 1/8 + 1/16 + 1/32+...

@InDstructR

5 жыл бұрын

@ki kus won't stop me, And when he writes 1/8 he's abbreviating 1/16+1/32+1/64+1/128+...

@shounakghosh8595

5 жыл бұрын

Whoa that converged quickly

0:10 is this a pewdiepie reference? 😂😂

@albel2094

5 жыл бұрын

He liked it!!!

@randomdude9135

4 жыл бұрын

@@albel2094 yupp

@randomdude9135

4 жыл бұрын

Yupp

I remember solving this exact question in my JEE ( Mains ) exam.

@classicmelodyvetrivel710

2 жыл бұрын

@Sanat R mains usually has easy questions

@Avighna

Жыл бұрын

@Sanat R - Study Vlogs Sure, yeah, "easy question" 😬

@Avighna

Жыл бұрын

@Sanat R - Study Vlogs Woah, really? What kinda questions do they ask? Could you send me a link?

5:48 “Back in my day kids would use *ALGEBRA* but now their brains are rotting from these darn *CALCULATORS* ”

1 + 1 = 3 And sinx/n=six=6.

@rio_agustian_

5 жыл бұрын

You stupid, 1 + 1 ≠ 3 3 = 2 + 1 π = 2 + 1 π - 1 = 2

@CookieJar2025

5 жыл бұрын

@@rio_agustian_ so π = 3 lol nice discovery

@Kevin-14

5 жыл бұрын

@@CookieJar2025 e = 3 = π

@SameerKhan-nd5qb

5 жыл бұрын

@@rio_agustian_ noob

@SameerKhan-nd5qb

5 жыл бұрын

@@Kevin-14 lool nooob

Take x ^2 + 3x = a Then in step 2 a(a+2) + 1 a^2 + 2a + 1 = (a+1)^2

@mat1305h

5 жыл бұрын

Yes much easier, and you see it imediatly too.

@Polarspy

5 жыл бұрын

was about to say this, i think it's a lot more intuitive

@milanmitreski7657

5 жыл бұрын

Isn't it beautiful how one problem can be solved in diffrent ways, even if the idea and the method are nearly the same. That's why we love maths.

@sanjaisrao484

5 жыл бұрын

@@milanmitreski7657 Yes

@akshetpatial5466

5 жыл бұрын

You extra smart boy the time required here will be same

Sorry...Time over! give me your exam!

This is beautiful. I've been looking at it for five hours now

now do it with CALCULUS

@davidappell3105

3 жыл бұрын

Why do you think this is funny?

@gabrielpinhal8325

3 жыл бұрын

@@davidappell3105 because suffering is funny

@sanchit6107

2 жыл бұрын

@@davidappell3105 Its FUNI

0:09 That was PowerFul

Not only 2 = 1+1, but also 0 = 1-1. From the second row: (x^2+3x+1-1)(x^2+3x+1+1)+1 and per the third binomial equation = (x^2+3x+1)^2 -1^2 +1 = (x^2+3x+1)^2

@etemkaandelibas3649

5 жыл бұрын

I didn't understand. Where did you use binomial expansion

@jinja3113

5 жыл бұрын

0 = 1-1 1 = 1*1 2= 1+1

@yogeshpathak73

4 жыл бұрын

I didn't see any binomial here... But what i see is that you used the form (a+1)(a-1) + 1 = a^2 - 1 +1= a^2

@Bayerwaldler

4 жыл бұрын

@@yogeshpathak73 I think Tibor Grün is from Germany. In German school curriculum the formula (a+b)*(a-b) = a^2 - b^2 is known as 3. binomial formula. b=1 is a special case.

@yogeshpathak73

4 жыл бұрын

Oh ok... Didn't know that. Thanks.

Nice. I did it this way: Assume that the expression is a square number so: x(x+1)(x+2)(x+3)+1 = n^2 x(x+1)(x+2)(x+3) = n^2 - 1 x(x+1)(x+2)(x+3) = (n+1)(n-1) What I did then is realise that the factors of the product on the right differ by 2. Playing around you can find that: x(x+3) = x^2+3x = n-1 (x+1)(x+2)=x^2+3x+2 = n+1 So n = x^2 + 3x + 1 Not as neat as your method though! Thanks for the video

@juanbomfim22

5 жыл бұрын

OMG ive almost done it completely. i just stopped at (n+1)(n-1) lol WD! i mean 'not that almost' lmao

@joshuamason2227

5 жыл бұрын

How do I play around with it

@dr3w199

5 жыл бұрын

@@joshuamason2227 Well you have the product of 3 binomials and a monomial for which we can multiply in any order. If you try a few cases, or think about it you spot that x(x+3) and (x+1)(x+2) have a difference of 2.

@joshuamason2227

5 жыл бұрын

@@dr3w199 okie

@sunnykarwani3556

3 жыл бұрын

Damn... It's a great method. Neat work. 💯

0:01 that's my life philosophy now

i remember my math teacher asking me to prove that n(n+1)(n+2)(n+3) + 1 is always a perfect square given that n is an integer

I'm only in 8th grade Algebra 1 but I was using variables to find how some of your factorizations works. You went from (x^2+3x)(x^2+3x+2)+1 to (x^2+3x)(x^2+3x+1)+(x^2+3x+1). What I did was set (x^2+3x) to a variable (a). (a)(a+2)+1 a^2+2a+1 (a+1)(a+1) Now substitute back in. (x^2+3x+1)(x^2+3x+1) When in doubt use variables..

@trueriver1950

4 жыл бұрын

Yes, that's using even more algebra than BPRP did.

@zocker2586

4 жыл бұрын

Well yes because using the variables is actually the logic behind the solution, it's just that it was invisible throughout the process :D

@baranibarani4970

4 жыл бұрын

Where r u from?

@sanjanabiswas9774

3 жыл бұрын

Agreed! Variables always help to proceed the solution.

@enricomassignani

3 жыл бұрын

I put x=500 but multiplied everything. In the end i got to sqrt((x+y)^2) with x=500 and y=501^2

I chose to make x = 502, which ends up yielding a nice difference of squares and a two term quadratic, which is much easier to distribute. The quartic you get has a palindromic pattern reminiscent of pure binomial coefficients, making it tempting to say the golden ratio is a root. It is, in fact, a root, so synthetically divide the quartic by the golden ratio identifying polynomial, x² - x - 1. You end up with the golden ratio identifying polynomial again, meaning that the original quartic in that square root is (x² - x - 1)², so cancel the power and the root. Plug 502 back in for x, some quick multiplying and subtracting by hand and you've got 251501.

Continueing from: sqrt( (x^2 + 3x) (x^2 + 3x + 2) + 1 ) let y = x^2 + 3x sqrt( y * (y + 1) + 1 ) = sqrt( y^2 + y + 1 ) = sqrt( (y+1)^2 ) = y + 1 = x^2 + 3x + 1 = (x + 1) (x + 2) - 1 = 501 * 502 - 1 = 251501 much easier to multiply :p

@razvy3827

Жыл бұрын

that is what i wanted ti type nice 👍

You can also put a +1-1 inside the x^2+3x bracket and it'll be in the form of (a+b)(a-b).

@kilindogma9711

5 жыл бұрын

that's what i thought he was gonna do as well but what he did was cool as well.

@ssdd9911

5 жыл бұрын

why?

@iabervon

5 жыл бұрын

Yeah, (x-1)(x+1)+1=x^2-1^2+1 seems easier to find than multiplying out exactly the right portion of the big expression.

I love this. You did a great job of laying out a good challenge.

Blew my mind! Earned yourself a new subscriber! Keep up the good work!👍

Every body knows 1+1=2 but i know 1+1 =/= 3

@blackpenredpen

5 жыл бұрын

♫♪Ludwig van Beethoven♪♫ Hahahhaha

@jgsh8062

3 жыл бұрын

I’ve got you all beat with 1+1 > 0

@JDguy11222

3 жыл бұрын

@@jgsh8062 nah mine's better 1+1≠1+1

Really good solution! GOOD Teacher👍

a very good perspective and a very good solution. thank you!!!

Why are your videos so entertaining? I'm so glad I came across this channel.

3:20 I solved it differently. Let y= x^2+3x. Then substitute y into the expression making y(y+2)+1, distribute so y^2+2y+1 and that is a perfect square of (y+1)^2. Here, the square root and exponent cancel each other leaving y+1, sub back in x and then easily find the answer :)

@matthewmanzanares6798

Жыл бұрын

this is also what I did and I think that this is a bit better because you don't have to split 2 into 1 + 1 and do the rest

@cheesecircle3033

8 ай бұрын

That's what I did as well

What a incredible content. Im a student of math (i'll be a teacher in the future) from Brazil. Thank you so much for sharing knowledge!

Your explanation is awesome . I like your teaching very much. Thanks

I expressed it as sqrt((501.5-1.5)(501.5-0.5)(501.5+0.5)(501.5+1.5)+1) You get two a^2-b^2 expressions that you can multiply out, add the 1, and then factor into a squared quadratic expression Very neat and, as someone mentioned elsewhere, it generalizes to “1 plus the product of any four consecutive integers is a perfect square”

I am so impressed with myself, I actually used the same method you did before watching the video =D

@blackpenredpen

5 жыл бұрын

Jan Wrobel nice!!!!

Everybody knows e^{iτ}=1 . . . . But I know 1=e^{iτ}

@blackpenredpen

5 жыл бұрын

Nice!!!

@paawanjethva

5 жыл бұрын

@@user-bd9mu3ee1i That's e^{iπ}. τ=2π

@fgvcosmic6752

5 жыл бұрын

My mans using tau! Up top!

@peterg644

4 жыл бұрын

@@user-bd9mu3ee1i he's using tau not pi

This just blowed my mind!!! Love this

That was beautiful. Thank you.

The world needs more teachers like you. I'm more impressed by your teaching skills than any math. Much respect.

Now this video makes me like algebra

@FermionClasses

3 жыл бұрын

kzread.info/dash/bejne/ioxmpqtydZTghps.html

This was fantastic. I wish to thank you for your videos.

Really good video. Thanks for inspiring students. Keep it up

3:20 just put y = x^2 + 3x, then you have y(y+2) + 1 = y^2 + 2y + 1 = (y+1)^2. So the answer is y + 1, or x^2 + 3x + 1.

@cypherx7247

5 жыл бұрын

I also did it in this way...but that way was also fine...its all about which method comes in your head first

@lasergamer2869

3 жыл бұрын

Dang that’s genius

I love the explanation, though I did it a bit differently. When I got to the second line, I substituted (x²+3x) as y and found that that worked much simpler than distributing 2 as 1+1.

Seemingly elementary problems can have wonderfully elegant solutions! All we need is to substitute a number with x, and the magic begins.

i watched this video this video right before my math competition and the same type of question came up on the task sheet. Thank you very much!

@bucinoulje7505

3 жыл бұрын

for those wondering the question was 202120212019(202120212021)(202120212023) all over 100010001 x (202120212021 squared +4)

I did assume there was a nice solution, but expanding under the root to get x^4 + 6x^3 + 11x^2 + 6x + 1 was pretty easy, and then matching coefficients in (x^2 + ax + 1)^2 was straightforward too. But yeah, the main thing is to replace 500 by x. I don't think I could intuitively see which two of the brackets would make it easier, and I'm not sure that's a better method than expanding the whole thing to only 4 terms (plus the one on the outside).

please give an example differentiation of complex functions

I love you, you make me remember stuff I had forgotten!

You are an absolute genius bro🤟🤟 I was surprised by your last step result 😱😱😱

Doing a PhD in Literary Studies, but stuff like this is why I absolutely love maths ♥

There are things to learn from each of your videos 😁❤️

@deadvirgin428

5 ай бұрын

Well yes, that's the point.

Nice... Great method of solving

Nice video . I learnt a lot

I know this kind of the prob, i use (n+1)(n+2)-1

Nice factoring method but it might have taken me a while to spot. Multiplying out and factoring isn't so bad (x - 1)x(x + 1)(x + 2) + 1 = (x^2 - 1)(x^2 + 2x) + 1 = x^4 + 2x^3 - x^2 - 2x + 1 = (x^2 + bx +- 1)^2 = x^4 + 2bx^3 + (b^2 +- 2)x^2 +- 2bx + 1 We see this works if b = 1 and c = -1 so the answer is 501^2 + 501 - 1 = 500^2 + 2*500 + 1 + 500 = 251501

Awesome solution to the question

@4:15 wow I did not see it coming! Really good thank you!

You can also this as x^2+3x=t and expression would become t(t+2)+1 =(t+1)^2 this que came in practice test for jee last week And guess what i solved that 😎😎😎👍👍

I love your videos about not using calculators (Like the Wolfram-Alpha video)! They're the best! Keep up the good work! It's nice going back to algebra sometimes...

@blackpenredpen

5 жыл бұрын

Why It? Yea me too. I try to mix things up a bit.

3:32 perhaps an easier method to spot is if you partially expand the brackets so that you end up with (x²+3x)² + 2(x²+3x) + 1, which is precisely (x²+3x+1)²

Very interesting calculation!

Shout-out to my colorblind fam who can never tell when he switches pens

I know this is not related to this video but I wanted to post this on a new video so you might see it :) your trick for integrals of thinking "wouldn't it be nice if..." has helped me so so much, so thank you :) love your videos!

@blackpenredpen

5 жыл бұрын

Awww thank you!!!!!

man this was amazing to watch! so clever!

This is very useful, I’m trying to think more outside the the box for hard mathematical equations either for proofs or something like this, I didn’t thing to make 500 = x, but it simplified it so much. This is a useful skill and I will be sure to use it

Dude, I always had a good grasp on algebra as a kid and in highschool I always aced most algebra, but somehow my teachers (and I) missed this property of algebraic equations. So freaking cool. It has been nigh on 15 years since high school, but I am still learning new and cool algebra. Thanks so much blackpenredpen!

"And now, here's the deal"… You know that when he pronounces that phrase things are 'bout to get complicated.

Actually trying it out was fun, and there was some surprisingly elegant generalization going on behind the scenes.

It is so interesting and good to remember. Thanks.

Everybody know e^2.pi.i = 1 . . But I know 1 = e^2.pi.i

@mundane3809

5 жыл бұрын

Wrong it's - (e ^ pi × i)

@nikolas9105

5 жыл бұрын

@@mundane3809 Nice try but thats -1 ignoring your name

@mundane3809

5 жыл бұрын

@@nikolas9105 no e ^ ( pi × i ) = -1 So if you make -1 negative, it become positive.

@RunstarHomer

5 жыл бұрын

@@mundane3809 you are correct but the original comment was also correct. e^2πi = 1.

@mundane3809

5 жыл бұрын

@@RunstarHomer oof yea it's actually correct. sorry for the mistake!

I understood everything until the bit at 4:35 - 5:04 What do you mean by "factoring out"?

@AE-rg5rc

5 жыл бұрын

When a number repeats itself in an addition you can factor it out, basically do the inverse of distributive property. So we have x²+3x+1 repeating in both therms. You can factor it out and you will be left with x²+3x+1 ( x²+3x +1), equivalent to x²+3x+1( x²+3x) + x²+3x+1 (1)

@leif1075

5 жыл бұрын

@@AE-rg5rc but thats just squaring it and you don't have two of the sake expression..you don't jave twobx squared plus 3x plus 2 you only,have one

@ViratKohli-jj3wj

4 жыл бұрын

@@leif1075 please Learn some math, this is for grade 6 atleast in asian countries.

@leif1075

4 жыл бұрын

@@ViratKohli-jj3wj I know some math, thanks very much..I had a valid question

When he drops the "Check this out", you know crazy stuff will happen on the board

More impressed with how someone came up with the question

What Everybody knows : 1+1=2 What BPRP knows : 2=1+1 . . . . . What I know : 1+1=2 and 2=1+1 😇😇😇😇😇😇😇😇😇😇😇

I'm doing this on the toilet, so I only hope I'm starting correctly, with (500)(502)=(501²-1) and (501)(503)=(502²-1) But then again, we could cheat and go with (501)(502)=(501½²-¼) and (500)(503)=(501½²-9/4)?

WOW! Now that's an amazing way to solve it!

At 3:45, you could also treat the first factor as (x^2+3x+1-1) so together with the second factor you have (x^2+3x+1-1)(x^2+3x+1+1) = difference of squares ((x^2+3x+1)^2 - 1. Plus the extra 1 on the outside you get the perfect square.

this guy is a genius!

Wow your method and my method are similar .....I had take the whole expression as y and then square it and then assume x to be 500 and multiplied and had taken x^2+3x to be z and at end I got y=z+1 that is y = x^2 + 3x + 1 and it's done

Brilliant solution .keep it up

This was a great explanation

I have never been so hyped at 2 = 1+1 before.

Why I shouldn't belive my calculator? It gave me the answer as 251501 Edit: I never had that much likes in my life

@aifesolenopsisgomez605

5 жыл бұрын

but... was it fun?

@JohnSmith-kb4re

5 жыл бұрын

@@aifesolenopsisgomez605 Fun is not something one considers when wrestling with numbers, but this... Does put a smile on my face.

@Meteo_sauce

5 жыл бұрын

Because in exams, you get your marks based on working and not on the answer

@matbronk1

5 жыл бұрын

I think he meant that algebra is more useful than a calculator. The title doesn't read "you shouldn't believe your calculator", it says you shouldn't believe IN your calculator, and rather resort to algebra instead.

@mdaslamhayat627

5 жыл бұрын

LOL, Wasn't expecting that much comments, sure algebra is better than directly using calculator and is more enjoyable to do so , but it took me time to realize what he meant. Besides, I am a 7th grader, so calculator is not allowed in school for us. We can use from 9th grade.

The entry was epic and the whole video is interesting.

Thank u very much i couldn't ever solve it without ur help...and i like the way you analize and explain every Q. In such away that a child also can find it helping...and i got ur ans.. Bro🙏

Him: Starts the video with 1+1=2 Me: *ok we are getting somewhere now

BPRP know 2 = 1+1 I know 2 = 2 what happened to the comment button its gray

@jinja3113

5 жыл бұрын

I know 2 = two

Very elegant solution

I did it by recognizing that (x^2+3x)(x^2+3x+2) is easily simplified with a substitution of y=(x^2+3x+1). It simplifies to (y-1)(y+1) = y^2 - 1. Since we have a "+1" hanging out after the 4-term product, that gets rid of the "-1" in our simplified expression, yielding just y^2 under the radical sign. square root of y^2 = y. That means the solution is our substitution: y=(x^2+3x+1). Plugging in 500 for x gives us 251501.

Just do the multiplication by hand.

Hmmm ive got an easier way when you use 1 + 1 instead of 2 Here is how I do according to you: (x^2+3x+2)(x^2+3x+1) =(x^2+3x)^2 +2 then √((x^2+3x)^2 +2) = x^2+3x+1

@XWurstbrotX

5 жыл бұрын

You can't solve squareroots of sums like that, eventhought your result is correct.

Man, you deserve more subs!

wow, just wow!! Fascinating !!