Question

What is the substitution should be used to rewrite x^8 -3x^4 + 2 =0

Answer 1

get into ax²+bx+c=0 form

subsitute u=x⁴

x⁸-3x⁴+2=0
(x⁴)²-3(x⁴)+2=0
u²-3u+2=0
factor
(u-2)(u-1)=0
set to zero

u-2=0
u=2

u-1=0
u=1


wait, u=x⁴

2=x⁴

`\sqrt[4]{2}=x`

1=x⁴
+/-1=x


the subsitution is u=x⁴
and the possible values for x are -1,
`\sqrt[4]{2}=x`, and 1