Question

Solve for x²-2 [a²+b²]x+[a²-b²]² = 0

Answer 1

hope you get the answer

Answer 2

Given :  x² - 2(a² + b²) + (a²  - b²)² = 0

To Find :  Solve for x

Solution:

x² - 2(a² + b²) + (a²  - b²)² = 0

(x - y)² = (x + y)² - 4xy

=>  x² - 2(a² + b²) + (a² + b²)² - 4a²b² = 0

(x -y)² = x² - 2xy + y²

=>  (x  -  (a² + b²))² - (2ab)² = 0

x² - y²  = (x + y)(x - y)

=> ( x  -  (a² + b²) + 2ab)  ( ( x  -  (a² + b²) - 2ab)  = 0

=> (x - ( a² + b² - 2ab)) ( x - (a² + b²+2ab)) = 0

=> ( x  - (a - b)²)(x - (a + b)²) = 0

=>  x=  (a - b)² , (a + b)²

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