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)

a

step-by-step explanation:

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