Which are the solutions of the equation x^4 – 5x^2 – 36 = 0

Question

Which are the solutions of the equation x^4 – 5x^2 – 36 = 0

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Amara 1 month 2021-10-12T09:01:54+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-12T09:03:08+00:00

    Answer:

    x = ± 3, x = ± 2i

    Step-by-step explanation:

    Given

    x^{4} – 5x² – 36 = 0

    Use the substitution u = x² then the equation is

    u² – 5u – 36 = 0 ← in standard form

    (u – 9)(u + 4) = 0 ← in factored form

    Equate each factor to zero and solve for u

    u – 9 = 0 ⇒ u = 9

    u + 4 = 0 ⇒ u = – 4

    This indicates there will be 2 real roots and 2 complex roots

    Change back to find values of x, that is

    u = 9 ⇒ x² = 9 ⇒ x = ± \sqrt{9} = ± 3 ← real roots

    u = – 4 ⇒ x² = – 4 ⇒ x = ± \sqrt{-4} = ± 2i ← imaginary roots

    0
    2021-10-12T09:03:41+00:00

    4x-10x = 36
    -6x = 36
    X= -6

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