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

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  1. 21 May, 11:57
    0
    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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