Answer:
Replace x^2 with m
Step-by-step explanation:
x^8-3x^4+2=0
We want to write this as a quadratic, which means as am^2+bm +c
x^8 needs to become m^2
Let m = x^4
Then m^2 = x^4^2 = x^8
Our equation becomes
m^2 -3m +2 =0
Replace x^2 with m
Answer:
Replace x with [tex]y^{1/4}[/tex]
Step-by-step explanation:
The general form of a quadratic equation is [tex]ax^{2}[/tex] + bx + c.
To find a substitution we have to think of a way of substituting ‘x’ to make it have a power of 2,
Here, we will use [tex]y^{1/4}[/tex]
[tex]x^{8}[/tex] - [tex]3x^{4}[/tex] +2 = 0
let x = [tex]y^{1/4}[/tex]
so it gives
([tex]y^{1/4}[/tex])^8 – 3( [tex]y^{1/4}[/tex] )^4 +2 = 0
[tex]y^{2}[/tex] – 3y + 2 = 0
Solving the equation
[tex]y^{2}[/tex] - 2y – y + 2 =0
([tex]y^{2}[/tex] – 2y) -1(y – 2) = 0
y(y - 2) -1(y - 2) = 0
(y-1) (y-2)
:- y = 1 or y = 2
Since x = [tex]y^{1/4}[/tex]
When y = 1
X = [tex]1^{1/4}[/tex]
X = [tex]4\sqrt{1}[/tex]
X = 1
and when y = 2
X = [tex]2^{1/4}[/tex]
X = [tex]4\sqrt{2}[/tex]
X = 1.1892...
