Question

Solve (3sqrtx^4-2x^2+1)+(2xsqrtx^4+2x^2-8)=(x^2+1)^2

Answer 1

3√(x^4-2x^2+1) + 2x√(x^4-2x^2-8) = (x^2+1)^2
Good luck with that. You will have to use some numeric solution method, It is a cubic function of x^2, so will very lilely have no rational solutions. In fact, wolframalpha.com says that all the roots are complex. See

https://www.wolframalpha.com/input/?i=3%E2%88%9A%28x%5E4-2x%5E2%2B1%29+%2B+2x%E2%88%9A%28x%5E4-2x%5E2-8%29+%3D+%28x%5E2%2B1%29%5E2

Answer 2

Um, it’s x^4+2x^2...but thanks anyway!

Answer 3

Oops. My bad. That makes quite a difference!
x=2
Use the steps I followed on the problem above this one.
Square both sides, collect terms, get the root all alone and square again. Lots of terms will vanish.

Come back if you get stuck.