solve for x x²-2(a²-b²)x + (a²-b²)²=0
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Answer:
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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