X^4-10x^2+21=0 factor using quadratic techniques

(x - sqrt (7)) (x + sqrt (7)) (x - sqrt (3)) (x + sqrt (3))

Step-by-step explanation:

x⁴ - 10x² + 21 = 0

Let t = x²

Then the equation becomes,

t² - 10t + 21 = 0

t² - 7t - 3t + 21 = 0

t (t - 7) - 3 (t - 7l

(t - 7) (t - 3)

Since t = x²,

(x² - 7) (x² - 3)

Using a² - b² = (a - b) (a + b)

(x - sqrt (7)) (x + sqrt (7)) (x - sqrt (3)) (x + sqrt (3))

sqrt : square root

x = + / - sqrt (7) & + / - sqrt (3)