Russia | Math Olympiad Algebra Power Question | Square Simplification | Find the Value of "x" ?

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[@schlingel0017]

Just opened the parantheses like a well-behaved kid and found the same answers 😜

[@MrGeorge1896]

It is easier to reduce the LHS to a common denominator first and then simplify:
16x² (2x² + 2*9) / (x² - 9)² = 32
x² (x² + 9) = (x² - 9)²
x⁴ + 9x² = x⁴ - 18x² + 81
27x² = 81
x² = 3
x = ±√3

[@NadiehFan]

Exactly. That was also my solution without first watching the video. Solved within a minute.

[@samueldeandrade8535]

Yeah. He knows that. But this is a fake math channel.

[@walterwen2975]

Math Olympiad: [4x/(x + 3)]² + [4x/(x - 3)]² = 32; x = ?
(4x)²[(x - 3)² + (x + 3)²]/[(x + 3)(x - 3)]² = [32(x⁴ + 9x²)]/[(x² - 9)²] = 32
x² ≠ 9; x⁴ + 9x² = (x² - 9)² = x⁴ - 18x² + 81, 27x² = 81, x² = 3; x = ± √3
Answer check:
[4x/(x + 3)]² + [4x/(x - 3)]² = [(32x²)(x² + 9)]/[(x² - 9)²]
[32(3)(3 + 9)]/[(3 - 9)²] = [32(3)(12)]/36 = 32; Confirmed
Final answer:
x = √3 or x = - √3

[@АндрейПергаев-з4н]

Все гораздо проще
(4х)^2*(1/(х-3)^2+1/(х+3)^2)=32
х^2*(2*(х^2+9)/(х^2-9)^2=2
Пусть х^2=а
а(а+9)=(а-9)^2
а^2+9а=а^2-18а+81
3а=9
а=3
х=-sqrt3, x=sqrt3

[@davidshen5916]

（1/（1+3/X））^2+（1/（1-3/X））^2=2， A=1+3/X， B=1-3/X， A+B=2， 1/A^2+1/B^2=2，A^2+B^2=2（AB）^2， 4-2（AB）=2（AB）^2， T=AB， T^2+T-2=0， （T-1）（T+2）=0，