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