Question

What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?

Answer 1

Substitute y for x^4.

Explanation:

Let y = x^4 then:

y^2 - 3y + 2 = 0.

Answer 2

`y^2 - 3y + 2 =0` is the required quadratic equation.

Explanation:

We are given the following equation in the question:

`x^8 - 3x^4 + 2 =0`

We need to make a substitution such that the above equation becomes a quadratic equation.

We make the substitution
`y = x^4`

`x^8 - 3x^4 + 2 =0\\\Rightarrow (x^4)^2 - 3x^4 + 2 = 0\\\Rightarrow y^2 - 3y + 2 =0`

`y^2 - 3y + 2 =0` is the required quadratic equation.