Math problem

Question

Find all solutions of:  x^4+2x^2-15=0

Answer 1

A 4th power is the square of a square, so we can first factor it out like a quadratic equation:

 

x^4+2x^2-15=0

(x² - 3)(x² + 5) = 0

 

(x² - 3) is the difference between two squares, so:

 

(x + √3)(x - √3)(x² + 5) = 0

 

x² cannot be negative, so we can't go any farther with  (x² + 5).

 

So our solutions are √3 and -√3