SOLUTION: practice problem that is confusing me, I thought quadratic equation was x^2 not x^4 so HELP please. x^4-10x^2+9=0

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Question 82627: practice problem that is confusing me, I thought quadratic equation was x^2 not x^4 so HELP please.
x^4-10x^2+9=0
Found 2 solutions by kev82, scott8148:
Answer by kev82(148) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,

You're right. This isn't a quadratic equation. But, we can turn it into one with a simple substitution. If I let then . Replacing x with q gives:



This is quadratic in q and can be factorised . So we have two solutions for q. But remember . So for both values of q we have a quadratic in x. Solving these should give you the final answers of x=-3,3,-1,1. If you can't get that, write back and I'll go over the working in more detail.

Hope that helps,
Kev

Answer by scott8148(5885) About Me  (Show Source):
You can put this solution on YOUR website!
this is a quadratic in (x^2) ... rewriting will help clarify ... (x^2)^2-10(x^2)+9=0

factoring gives ((x^2)-9)((x^2)-1)=0 ... factoring again gives (x+3)(x-3)(x+1)(x-1)=0

so x=-3, x=3, x=-1, x=1