????

Dear Student

Solution of ax^2+ bx+c=0  ==> (b +/- sqrt (b^2-4ac))/2a

Basec on the same formula

4x²-2(a²+b²)x+a²b².=0

X={   -(2(a²+b²)) +/-  [ 4(a²+b²)² - 4X 4Xa²b² ] } / (2X4)

={   -(2(a²+b²)) +/-2 [ a⁴+b⁴-2a²b² ] } / 8

={   -(2(a²+b²)) +/-2 [ (a²-b²) ] } / 8

={   -(a²+b²) +/- [ (a²-b²)² ] } / 4

={   -(a²+b²) +/-  (a²-b²) } / 4

==> the two solutions are 

X=   {   -a²-b² + a²-b²} / 4    ;    {   -a²-b² -  a²+b² } / 4

X= -b² / 2   ;   -a² / 2   ;  

Regards

Team

Topperlearning