That algebraic method isn’t a method at all. You can’t set off on a series of substitutions in the hope that you might end up with an easily recognizable perfect square. The “problem” has been constructed from the “solution”.

@YAWTon

11 күн бұрын

I disagree. Once that it is recognized that 64^2+49^2+15^4 has the form x^4+y^4+(x+y)^4 the result follows from straightforward algebraic transformations. No guessing involved. Of course, in the absence of this insight, it is also not difficult to use basic arithmetic to obtain the result 169.

@richardatkinson4710

11 күн бұрын

@@YAWTon You are right, but my point is that the “method” outlined does not mention that insight. The double substitution is totally unnecessary. (Do you agree?) You either notice that you can factorise, in which case you should (and you did - as did I when I saw this) or you go through the arithmetic.

@richardatkinson4710

11 күн бұрын

@@YAWTon It’s over 50 years since I did any maths, but the substitutions vaguely recalled the solution to the general quartic. Is that how the “problem” was conceived, do you think?

@YAWTon

11 күн бұрын

@@richardatkinson4710 I agree that his presentation was bad for the reasons that tou mentioned. Too many intermediary steps. Apparently the problem suggests a "solution" that is invalid, but leads to the correct value (based on the assumption that the squareroot of a sum equals the sum of the squareroots of the terms of the sum).

@LuluLaSaumure

6 күн бұрын

It is a math olympiad problem ! Of course, the problem has been built from the solution : it is meant to be solved this way. This is how the math olympiad jury makes to find the best students : by their abylity to find the right substitution at the right moment of the calculus and their ability to lead such a huge calculus until its end ! In real life maths, you hardly find such calculus but in a maths competition it's classic that people have to use such tricks

I guess calculating it directly would take less time.

@oboumami6186

7 күн бұрын

You are absolutely right, it is around eight times faster.

This is Candido's identity in disguise, [x^2 + y^2 + (x+y)^2]^2 = 2[x^4 + y^4 + (x+y)^4]. Candido used the Fibonacci numbers in his original publication.

The fourth root would have allowed for an extra simplification, giving 13 as the final result 😊

Haven't been doing this for more than thirty years ... and never missed it. 🙂

Why not just long multiply, add, divide by 2 and then find the square root? Much simpler.

If you took the square root and simplified the values under the radical sign, you will get: (sqrt(64)^2) = 64 (sqrt(49)^2) = 49 (sqrt(15)^4) = 15^2 = 225 64 + 49 + 225 338 ---------------------- = ------- = 169 2 2 The answer is 169

Excellent. Thank you.

169 is 13^2, so is there further simplification to be done at the 8^2 + 7^2 + 8 x 7 stage?

Nice. Elegant.

There is no need to open the paranthesis of 4th power. You could do the second substition before that.

I think the power of math practice is working these out long hand, verbally calling out as you go, with pencil on paper. You develop so many other skills through this process. Agreed time consuming but worth the time especially if you are a slower learner.

Прекрасная задача и великолепное объяснение ее решения. Мне 72 года и моя профессия не связана с математикой, но мне все понятно и интересно. СПАСИБО

Nice

@learncommunolizer

Ай бұрын

Thank you very much!

Siento que la pudo resolver fácilmente desde un inicio sin tanto rollo.

That would give me writers cramp.....and why would I ever need to do it....

Is this a solution or substantiation?

Vamos a resolver el problema paso a paso.Primero, definimos la operación:[ \sqrt{\frac{64^2 + 49^2 + 15^4}{2}} ]Calculamos cada potencia:[ 64^2 = 64 \times 64 = 4096 ][ 49^2 = 49 \times 49 = 2401 ][ 15^4 = 15 \times 15 \times 15 \times 15 = (15^2)^2 = 225^2 = 50625 ]Sumamos los resultados obtenidos:[ 4096 + 2401 + 50625 = 57122 ]Dividimos la suma por 2:[ \frac{57122}{2} = 28561 ]Calculamos la raíz cuadrada del resultado:[ \sqrt{28561} = 169 ]Entonces, la respuesta es:[ \boxed{169} ]

The solution made the problem seem more complicated. I don’t need a calculator nor do I need to use this method to find the same exact answer.

A nice radical math complication.

Супер мега задача! Thank you so much for it! It's perfectly cool

@learncommunolizer

Ай бұрын

Thank you very much!

Ow! My brain!

Should've used a^2 + b^2 + c^2 form

Was the first substitution necessary ?

@bvenable78

Ай бұрын

No substitutions are _necessary_; they just make the algebra easier. I like that he did the two substitutions; it breaks the problem down into smaller steps, making it more accessible to viewers - especially those that aren't practiced enough at algebra to follow skipped steps.

169 = 13^2 = 8^3 - 7^3

Step seven you forgot the clouser ')' but it doesn't affect the final answer.thanks for the solution....😊

Cool. I loved it.

Brilliant!

Surprised he didn’t end it with 169 = 13^2

@richardatkinson4710

16 күн бұрын

Or start with root root…

Математика как Поэзия! Им ночью снятся Арктики и Звездные Галактики, ведь математик- это Фантазёр!

OMG

Икату жжот. Зачот )

169. 5 minutes in mind.

Математика это жизнь!!!

Good old Pascal

Wer brauch sowas

±169

Are you crazy? The solution is quite simple and take never a minute to solve: (64 + 49 + 225) / 2 = 169

Très astucieux. Bravo !

@learncommunolizer

Ай бұрын

Thank you very much!

13²

15× rootover 226..?

i ❤ Mathematics

140

169

SO SIMPLE. DO THIS AND DO IT IN YOUR HEAD. If you know the rules. Solved it my head in seconds. Here's how. The square root is basically x^1/2 so using distribution that kills 2 from each exponent leaving [(64+49+225)/2] = (338/2)= 162. Easy

@LarghettoCantabile

19 күн бұрын

An interesting coincidence insofar as generally the square root does not distribute over terms. The numbers were probably chosen precisely because this coincidence is a trap.

@ArturJarosik

17 күн бұрын

I've done it exactly the same.

Легче все перемножить , будет корень из 28561=169.

Ans = 169 or even 13^2

No, this is too long..sometimes question like this in a test only give you 1 to 2 minutes to solve,.

I have much better solution. Everybody knows that 64^2=4096. 49^2=2401 15^4=225^2=50625 Half sum of it is 28561, which is square of 169, also known fact.

@Swannerator

Ай бұрын

"Everybody knows that..." - tell us that you cheated and used a calculator without telling us that you cheated and used a calculator. 🤡

@anatolykatyshev9388

Ай бұрын

@@Swannerator Author also used calculator to find square roots of 64 and 49. It is not easier , than 64^2 and 49^2!

@olegkobyzev1884

Ай бұрын

⁠​⁠@@Swannerator no need in calculator, that numbers are small (easy to multiply in mind), and even if you not remember 169^2 you can just calculate it on paper.. every one knows

@maas_ter

Ай бұрын

​@@anatolykatyshev9388everyone knows sqrt of 64 and 49 💀

@gagwong8964

Ай бұрын

Concur, way much better than fiddling all that ↑↓←→abxy口O∆ around 🤦🏻‍♂️

Very nice

@learncommunolizer

Ай бұрын

So nice, Thank you very much!!!

Are we not doing √ as the last step to get ±169 as answer?🤔

@mickaelbazola849

Ай бұрын

No, a square of number is positive

@go_gazelle

Ай бұрын

In algebra, the radical sign typically indicates the positive root only. A ± sign in front would indicate both roots. (y = sqrt(x) has no negative values for y.) However, I wouldn't say it's wrong if you include -169 as a second answer. I actually like that since the problem presents as arithmetic.

@gagwong8964

Ай бұрын

Thank you both for clearing my doubt.🙏🏻 I indeed went back to read about the basics . It says something like this : square root of a number is always positive, only in functions or equations like y=x², x has two values, the positive and the negative.

@go_gazelle

Ай бұрын

@@gagwong8964 I think that's basically correct. But y = x² seems like a strange example. A better example would be 9 = x². Here x = ±3. Or a = x². Here x = ±sqrt(a). Whereas, y=x² should be interpreted as a function in which there are infinite values for x.

@richardatkinson4710

16 күн бұрын

@@go_gazelle Quadratic equations have two roots.

This is why I changed my major to music!

@loganshaw4527

28 күн бұрын

College mathematics is just different. I loved exponentials as a kid did not learn of the different elevations until later. I know equal and above but not not learn much of below. But only learned to the end of highschool.

328

The only mistake was canceling the root with the square. Should have been written with +/- (a+b).

Nice writing skills.😂

Prefiero seguir programando en asembler

Y no le veo ningún aporte a las matemáticas

Haaaaa bic mac

Moral: when learning math, don't use KZread. 😂

Giochi di teoria , con calcolatrice vai subito alla soluzione😊 comunque ottima conoscenza👍

120√2 solution 😢

So much simpler than using a calculator 😂

Another solution First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169 Can you do without pencil and paper?

@rcyu

Ай бұрын

Don't you have to distribute the square root to 2 as well?

@gagwong8964

Ай бұрын

√(a²+b²+c²) ≠ a+b+c

@marcherrmann9635

Ай бұрын

Pure coincidence?

@keescanalfp5143

Ай бұрын

​@@gagwong8964, in spite of all we see that it still works, at least for her.

sqr30705

Guys, I just took the sqrt and squared exponents and cancel them out, then it'll be 64+49+(15)^2/2 Secondly, 64+49+225/2 Lastly, 338/2 Now you have your answer of 169, i didn't even learn this at school yet💀

@phoebe543

Ай бұрын

The denominator wasn’t squared

@Swannerator

Ай бұрын

I hope you pay attention in Maths class when your class gets up to this. 🤦🏻‍♂️

@UniqueNewYork27

Ай бұрын

I didn't even learn this at school yet lol

@popolaminc6188

Ай бұрын

🤦‍♂️Unexplainble, but you got the right answer

@irenebeltranruiz3431

Ай бұрын

I did the same!

Thanks! Step 6 you lose )

I’m not advanced by any means but so many unnecessary steps. Neat little arithmetic problem though

i just removed the squares and made 15^2/2 i got the same answer lol

just calculated in my head and got the result of 169 without draw more than a full papersheet the root of 64 and 49 squared is just 64 and 49 plus 15 squared ist 225 338 half is 169 it was less than 1 minute

@Physics4every1

22 күн бұрын

Same here wrote my comment then came to see how other people are screwing this up.

asnwer=9 os isit

Too much steps

@bvenable78

Ай бұрын

I expect he did that for instructional purposes, and to make the solution accessible to viewers with less practice in algebra.

@Crusader-George

27 күн бұрын

not really, it's doable compared to sqrt thousands lol

why not first get rid of the square root bracket by reducing the numbers to 64 +49+15^2...add those then divide by 2 and you still get 169 and the square root of that is 13....

Can you go a little slower!

Too much paper its not simplifing

WFT? I DID IT IN 3 STEPS. 169

@marcherrmann9635

Ай бұрын

Elaborate further, please....

@RobbieIsbell

Ай бұрын

@@marcherrmann9635 Seriously? It's easy: First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169

@TonyQl

13 күн бұрын

@@RobbieIsbell you can’t do that because root of a + b is not equal to root a + root b

Toooooo long solution

I never understand why they add so many steps . Like all numbers are 2 or power of 2. They do it like pc's not stray from the way they learned it even if the solution is infront of them

This isn’t real math. It’s nothing more than merely recognizing patterns.

@jaywest84

10 күн бұрын

Math is all about recognizing patterns !

I'm sorry, but this is absolutely dubious click bait bullshit. The video has nothing to do with a serious mathematical solution algorithm. the solution only works for exactly these numbers. The task was developed backwards from the solution and is in no way transferable to another example.

This is a terrible question. Useless maths that not only teaches kids very little , but misleads them into thinking they should memorize the tree for (a+b)^n expansion. Memorization lacks mathematical elegance

@albirtarsha5370

13 күн бұрын

Sour grapes.

C'est pas 169. C'est 225.... (2x56) C'est pas 13 au carré mais 15 au carré..... Un peu de sérieux svp.

@user-rw9cm9hk7m

Ай бұрын

Le résultat final est bien 169.

@gerardphilippe5793

Ай бұрын

Une fois 56. Pas deux fois. C'est donc bien 169. Et pas 225

@unbeaunom

Ай бұрын

C’est souvent ceux qui reprennent les autres qui se trompent. Il faudrait formuler ceci en une équation.

@matbohman

Ай бұрын

Non. b = xy (pas 2xy).

@Crusader-George

27 күн бұрын

you're wrong

Finally, it.equals 13.

@bvenable78

Ай бұрын

Why are you taking the square root of his final answer?

@unbeaunom

Ай бұрын

Joke?