Question

Solve for x:

4xsquare-4asquarex+(araise4-braise4)=0​

Answer 1

4x^2 - 4a^2x + (a^4 - b^4) = 0

4x^2 - 4a^2x + (a^2 - b^2) (a^2 + b^2) = 0

4x^2 - 2(a^2 + b^2)x -2(a^2 - b^2)x + (a^2 - b^2) (a^2 + b^2) = 0

2x [ 2x - (a^2 + b^2) ] - (a^2 - b^2) [ 2x - (a^2 + b^2) ] = 0

$x = \frac{ {a}^{2} + \: {b}^{2} }{2} \: or \: x = \frac{ {a}^{2} - \: {b}^{2} }{2}$