My friend asked me for math help for her pre-calc class and I can't for the life of me do the problem--- I'm out of practice.
Solve for x:
x^4-3x^2+2=0.
Hi
What is needed here is some simple substitution
you have
$\displaystyle x^4-3x^2+2 = 0$
Replace $\displaystyle x^2$ with a dummy variable, lets call it $\displaystyle a$
Now $\displaystyle x^4-3x^2+2 = 0$ becomes $\displaystyle a^2-3a+2 = 0$
This is a simple quadratic
$\displaystyle a^2-3a+2 = 0$
$\displaystyle (a-2)(a-1)= 0$
By the null factor law
$\displaystyle a = 1,2$
but we are after $\displaystyle x$ so
$\displaystyle x^2 = 1,2 \Rightarrow x = \pm 1,\pm \sqrt{2}$
I still tried those and they aren't working.
When substituting 2 (for all intents and purposes it works for the -2 too because of the squaring...) the equation ends up being
2^4 - 3(2^2) +2 which is..
16-12+2
which is 6.
The 1, -1 do work, though. My brains are frieeeeed.