solve x^4+7x^2-18=0

Question

Solve the equation

Answer 1

The equation may be written as (x²)² + 7(x²) - 18 = 0

 

Let u = x².  Then u² + 7u - 18 = 0

 

                        (u+9)(u-2) = 0

 

                        u = -9 or u = 2

 

So, x² = -9 or x² = 2

 

      x = ±√(-9) or x = ±√2

 

      x = 3i, -3i, √2, -√2