Question

Solve the equation x^4+7x^2-18=0 and express each solution in a+bi form

Answer 1

Answer:

The following are the solutions found for x:

+√2 + 0i

-√2 + 0i

0 + 3i

0 - 3i

Step-by-step explanation:

The given equation is:

x⁴ + 7x² - 18 = 0

Rewrite x4 as (x²)²

(x²)² + 7x² − 18 = 0

Let u = x²

u² + 7u − 18 = 0

Factorize:

u² + 9u - 2u - 18 = 0

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

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

(x²-2)(x²+9) = 0

Seperate both equations:

x² - 2 = 0                     x² + 9 = 0

x = ±√2                       x = ±√-9

x = ±√2                       x = ± 3√-1

x = ±√2 + 0i                x = 0 ± 3i