Question

4x^2-4a^2-(a^4-b^4)^2 solve for x​

Answer 1

Answer:

4x²-4a²x+(a⁴-b⁴)=0

or, 4x²-2{(a²+b²)+(a²-b²)}x+(a²+b²)(a²-b²)=0

or, 4x²-2(a²+b²)x-2(a²-b²)x+(a²+b²)(a²-b²)=0

or, 2x{2x-(a²+b²)}-(a²-b²){2x-(a²+b²)}=0

or, {2x-(a²+b²)}{2x-(a²-b²)}=0

Either, 2x-(a²+b²)=0

or, 2x=a²+b²

or, x=(a²+b²)/2

Or, 2x-(a²-b²)=0

or, 2x=a²-b²

or, x=(a²-b²)/2

∴, x=(a²+b²)/2, (a²-b²)/2 Ans.