An Amazing Algebraic Puzzle | Calculator Not Allowed | Finding a & b

An Amazing Algebraic Puzzle | Calculator Not Allowed | Finding a & b

Welcome to another exciting algebra challenge! In this video, we'll tackle a nice algebra problem and simplify it without the use of calculators. Test your math skills and see if you can solve this problem step-by-step. Perfect for Math Olympiad preparation and anyone who loves a good brain teaser. Let's dive into the world of algebra and sharpen our problem-solving skills together. Don't forget to like, comment, and subscribe for more math challenges!

In this video, we cover:

Techniques for simplifying algebraic expressions
Step-by-step walkthroughs of challenging problems
Tips and tricks for mastering algebra without a calculator
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🎯 This video is perfect for students, math enthusiasts, or anyone seeking to sharpen their problem-solving skills and gain confidence in dealing with algebraic expressions.

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[gaiatetuya]

問題にa, bが自然数だと書いておく必要がある。でないと幾らでも実数のa, bが存在する。例えば 右辺 a=－7, b=－９でも与式は成り立つ。

[RyanLewis-Johnson-wqxs]

193=193 solution (a, b)=(9, 7), (-7, -9) final answer

[Quest]

a^3-b^3= 9^ 3- 7^3 i. e
(a;b)= (9; 7);(-7;-9 )

[RashmiRay-cy]

Let 9=x and 7 =y. Then, the LHS of the given equation can be written as [(x+y)^4 + x^4 +y^4]/[(x+y)^2 +x^2+y^2] = = [x^2+y^2+xy]^2/[x^2+y^2+xy] = x^2+y^2+xy = [x^3-y^3]/[x-y] = [9^3-7^3]/[9-7] = [9^3-7^3]/2. Comparing with the RHS of the given equation, a=9, b=7.

[gregevgeni]

An acquaintance identity,
a^4 + b^4 +( a +b)^4 =
= 2 (a^2 +b^2 + a b)^2 (#).
Here, the nominator become equal to
81^2 + 49^2 + 16^4 = 9^4+ 7^4+ 16^4 = 9^4 +49^4 +( 9+7)^4 =
2 (9^2 +7^2 +7•9)^2 due to (#) and
(9 + 7 = 16) (1)
The denominator become equal to
9^2 +7^2 +4^4 = 9^2 +7^2 + 16^2 =
=9^2 +7^2 + (7 +9 )^2 =
= 9^2 +7^2 + 7^2 + 9^2 + 2•7•9 =
= 2 (9^2 + 7^2 + 7•9) (2)
So the initial fraction written, due to (1) and (2),
(81^2 +49^2 +16^4)/(9^2 +7^2+4^4)
= 2(9^2 +7^2 + 7•9)^2 /2(9^2 +7^2 +7•9) = 9^2 +7^2 +7•9 = (9^3 -7^3)/2 =(a^3 -b^3)/2 => a = 9 and b = 7
{ We apply the identity
a^3 -b^3 = (a-b)(a^2 +b^2 +a•b) }.
Comment!
And a = -9 and b = -7 is too a solution.

[taniacsibi]

Sol. Sunt :(a, b ):(9, 7), (-7, -9). Rezolvarea ok