Question

Use quadratic techniques to solve x^4 - 6x^2 + 8 = 0.

Answer 1

Answer:x = +- 2 and x = +- √2

Explanation:

Let's covert x^4 - 6x^2 + 8 = 0 into quadratic equation.

Let e = x ^ 2

So,

(x^2)^2 - 6x^2 + 8 = 0

e^2 - 6e + 8 = 0

e^2 - 4e - 2e + 8 = 0

e( e - 4 ) -2( e - 4 )

( e - 4 ) ( e - 2 ) = 0

Either,

e - 4 = 0

x^2 - 4 = 0 ( REMEMBER THAT e= x^2)

x^2 = 4

x = +- 2

Or,

e - 2 = 0

x^2 = 2

x = +- √2