solution set

Question

x^4-x^2-6=0

Answer 1

The equation x⁴ - x² - 6 = 0

(x²)² - x² - 6 = 0

Let x² = X

Now the equation becomes X² - X - 6 = 0

• Factorize the above equation

X² - 3X + 2X - 6 = 0

X(X - 3) + 2(X - 3) = 0

(X - 3) (X + 2) = 0

Apply zero product property.

X - 3 = 0 and X + 2 = 0

X = 3 and X = - 2

Back substitute X = x²

x² = 3 and x² = - 2

• Now solve x² = 3

Apply squre root on each side.

x = √3

x = ± 1.732

• And solve x² = - 2

Apply squre root on each side.

x = √(- 2)

x = √(i² )(2)

x = ± 1.414 i

Solutions of the equation x⁴ - x² - 6 = 0 are at x = ± 1.732 and x = ± 1.414 i.