Soooo Sweet!!!!!!!!!!

Excellent! this gives a courage in solving math problems, thank you🙏

@JJONLINEMATHSCLASSchannel

13 сағат бұрын

Glad it was helpful!

It's much simpler and requires fewer steps to solve this equation by substituting one variable for {x} instead of two. Let's use substitute {x} with the letter {a} ONLY because substituting additional letters make the equation more complicated to solve and takes up much more time. √(x) + √(x - 3)= 3 Let a^2 = x and a^2 - 3= x - 3 a + √(a^2 - 3)= 3 √(a^2 - 3)= 3 - a (√(a^2 - 3))^2= (3 - a)^2 a^2 - 3= (3 - a)(3 - a) a^2 - 3= 9 - 6a + a^2 Cancel out a^2 on both sides of equal sign -3= 9 - 6a -12= -6a 2= a Recall that x=a^2 Therefore, x= 2^2 x = 4 is solution. Now let's check the solution. √(4)+√(4-3)=3 2+1=3 3=3

@dukemmerife9310

5 күн бұрын

Nice! It's not simpler or shorter. Just different.

@samueladler9080

5 күн бұрын

​@@dukemmerife9310in fact it is much simpler working with one variable tho the process may be long. This one is convoluted, and it is daunting. Her method is not bad at all but it looks like sending English to both Chinese and Japanese thru Malay and back into English. But his is English to Japanese and back to English. He was over elaborate. If y=sqrt(3-x) then by implication y²+3=x Substitute for x, we have sqrt(y²+3)+y=3 By rearranging, squaring both sides, grouping like term, we have y=1 So 1=sqrt(x-3),and squaring both sides we have 1+3=x=4

@JJONLINEMATHSCLASSchannel

5 күн бұрын

Wow! Thanks so much ❤️❤️

Check out my pattern √x + √x-3 = 3 Move √x to the other side √x-3 = 3-√x Square both sides x-3 = (3-√x)(3-√x) x -3 = 9- 6√x +x Collect like terms 6√x +x-x = 9+3 6√x =12 Divide through by 6 √x = 2 Square both sides x = 4

@JJONLINEMATHSCLASSchannel

5 күн бұрын

Wow! Thanks 🤝🤝🤝

Wow nice this is from a topic called surdic equations. 👍

@JJONLINEMATHSCLASSchannel

6 күн бұрын

Thanks

❤❤

@JJONLINEMATHSCLASSchannel

3 күн бұрын

❤️❤️

Thank you, excellent

@JJONLINEMATHSCLASSchannel

4 күн бұрын

U are welcome

You're not only beautiful but also genius.

@JJONLINEMATHSCLASSchannel

3 күн бұрын

Thanks for the compliment

Very clever.Could I have another hug please.!!

@JJONLINEMATHSCLASSchannel

5 күн бұрын

Hugs❤️❤️

Greetings. I do appreciate you sharing. However, I had great difficulty staying awake during the video, absolutely no fault of yours. I completely understand the concepts employed. Therefore, I did not have to see all your explanations. Your solution method is totally new to me. My approach is from x^1/2+(x-3)^1/2=3 we have x^1/2=3-(x-3)^1/2, (x^1/2)^2=((3-(x-3)^1/2))^2, x^2/2=3^2-2×3(x-3)^1/2+(x-3)^2/2, x=9-6(x-3)^1/2+x-3, x-x=9-3-6(x-3)^1/2, 0=6-6(x-3)^1/2, -6(x-3)^1/2=-6, -6(x-3)^1/2/-6=-6/-6, (x-3)^1/2=1, ((x-3)^1/2)^2=1^2, x-3=1 and x=1+3=4. Lovely.

@JJONLINEMATHSCLASSchannel

3 күн бұрын

🤝🤝

Alternatively say y = average of x and x-3 Then y = x-3/2; Back substituting we get sqr(y+3/2)+sqr(y-3/2)=3 By squaring both sides and rearrange terms We arrive at y= 5/2 from which x= 4

@JJONLINEMATHSCLASSchannel

3 күн бұрын

Thanks

Take root x to the right and sq both sides. Solve for x

It took me less than a minute to solve. √(x-3)=3-√x. x-3=9-6√x+x -12=-6√x 2=√x c=4

@JJONLINEMATHSCLASSchannel

5 күн бұрын

🤝🤝🤝

@denzilgounden4044

Күн бұрын

I've done the same

Merci bien

@JJONLINEMATHSCLASSchannel

4 күн бұрын

You are welcome

Thank-you, professor JJ for this hug.

@JJONLINEMATHSCLASSchannel

5 күн бұрын

U are welcome😃

The answer is 4 using quadratic formula

it is max 2 step problem, re-arrange and square both sides, twice.

@JJONLINEMATHSCLASSchannel

4 күн бұрын

Thanks

It IS necessary to detemine the domain of definition

@JJONLINEMATHSCLASSchannel

3 күн бұрын

Noted

4.

... sqrt(x) + sqrt(x - 3) = 3 ... Let sqrt(x) - sqrt(x - 3) = T ... [ sqrt(x) + sqrt(x - 3) ] * [sqrt(x) - sqrt(x- 3) ] = 3 * T ... x - (x - 3) = 3 * T ... T = 1 ... so Eq.(1) : sqrt(x) + sqrt(x - 3) = 3 & Eq.(2): sqrt(x) - sqrt(x - 3) = 1 ... after adding Eq.(1) and Eq.(2) we obtain ... 2 * sqrt(x) = 4 ... x = 4 ... finally checking x = 4 in original equation ... sqrt(4) + sqrt(1) = 3 ... S = { 4 } ... thanks JJ for sharing your interesting solution strategy ... take good care, Jan-W

@JJONLINEMATHSCLASSchannel

3 күн бұрын

U are welcome. Thanks for your contribution

@adamibrahimmuhammad5610

3 күн бұрын

????

Why is it that solving the value of X too long? √x + √(x-3) = 3 36x = 144 x = 4

@devonwilson5776

3 күн бұрын

Greetings. Where the 36x comes from?

It can be solved in 5 lines 😅