SOLUTION: X ^ 4 – 2 x ^ 2 = 8 That is: x to the fourth minus two x squared equals eight. Find all solutions for x. I have attempted this problem several times and am fighting with i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: X ^ 4 – 2 x ^ 2 = 8 That is: x to the fourth minus two x squared equals eight. Find all solutions for x. I have attempted this problem several times and am fighting with i      Log On


   



Question 204560: X ^ 4 – 2 x ^ 2 = 8
That is: x to the fourth minus two x squared equals eight.
Find all solutions for x.
I have attempted this problem several times and am fighting with it, I thought to take the square root of both sides and that didn't work, and I tried adding eight to both sides but I am still stuck and don't know how to proceed. Please help!

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
x%5E4-2x%5E2+=+8 Subtract 8 from both sides of the equation.
x%5E4-2x%5E2-8+=+0 Now you can make this look like a quadratic equation by temporarily substituting x%5E2+=+z
z%5E2-2z-8+=+0 Factor this.
%28z%2B2%29%28z-4%29+=+0 Apply the zero product rule.
z%2B2+=+0 or z-4+=+0 which means that...
z+=+-2 or z+=+4 Re-substitute z+=+x%5E2 to get:
x%5E2+=+-2 or x%5E2+=+4 so this means that...
x+=+sqrt%28-2%29 or x+=+-sqrt%28-2%29 or x+=+2 or x+=+-2