Question

1. Find the solutions of the equation x^4−x^2−12. Show your work.

Answer 1

Answer:
`x=\pm 2`

Explanation:

Given

`x^4-x^2-12=0`

Let
`x^2=y`

thus

`y^2-y-12=0`

splitting
`-y as -4 y+3 y`

`y^2-4y+3y-12=0`

`y(y-4)+3(y-4)=0`

`(y-4)(y+3)=0`

thus y=4 or y=-3 but y=-3 is not a solution because square of a number cannot be negative

thus
`x^2=4`

`x=\pm 2`