Question

Solve x^4 - 3x^2 +2 = 0 using substitution.

Answer 1

Answer:

x = ± 1 , x = ± $\sqrt{2}$

Step-by-step explanation:

Let u = x² , then

$x^{4}$ - 3x² + 2 = 0 , can be expressed as

u² - 3u + 2 = 0 ← in standard form

(u - 1)(u - 2) = 0 ← in factored form

Equate each factor to zero and solve for u

u - 1 = 0 ⇒ u = 1

u - 2 = 0 ⇒ u = 2

Change the variable u back to x

x² = 1 ( take square root of both sides )

x = ± 1

or

x² = 2 ( take square root of both sides )

x = ± $\sqrt{2}$