SOLUTION: x^4+x^2-12=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x^4+x^2-12=0      Log On


   

Question 882963: x^4+x^2-12=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You may find it easy to factor y%5E2%2By-12=%28y%2B4%29%28y-3%29 .
If you replace x%5E2 for y (and consequently x%5E4 for y%5E2 ),
you realize that x%5E4%2Bx%5E2-12=%28x%5E2%2B4%29%28x%5E2-3%29 and that
any solution to x%5E4%2Bx%5E2-12=0 is a solution to %28x%5E2%2B4%29%28x%5E2-3%29=0 and vice versa.
The only real solutions to %28x%5E2%2B4%29%28x%5E2-3%29=0 are
highlight%28x=sqrt%283%29%29 and highlight%28x=-sqrt%283%29%29 ,
which are the solutions to x%5E2-3=0 .
x%5E2%2B4=0 does not have any real solution.