Solve the equation

Question

x^4-10x^2+24=0

Answer 1

Factor the left side of the equation using FOIL.

 

(x² - 6)(x² - 4) = 0

 

 

Noticing that each factor is a difference in perfect squares,

 

(x + √6)(x - √6)(x + 2)(x - 2) = 0

 

 

Set each of these factor equal to zero and solve for x.

Answer 2

Factor the expression:

 

x⁴ - 10x² + 24 = (x² - 4)(x² - 6) = 0

 

Then factor the factors as differences of squares:

 

[(x - 2)(x + 2)] [(x - √6)(x + √6)] = 0

 

Solutions are x = 2, -2, √6, -√6.