What are the solution(s) of the equation? – 5×4 + 16x? + 32x= – 6×4 – 2×3

Question

What are the solution(s) of the equation?
– 5×4 + 16x? + 32x= – 6×4 – 2×3

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Nick 3 years 2021-07-29T19:18:21+00:00 1 Answers 13 views 0

Answers ( )

  1. Tryphena
    0
    2021-07-29T19:20:04+00:00
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    Answer:

    The solutions are:

    x=0, x=-2, x=4i, x=-4i

    Step-by-step explanation:

    We need to find solutions of the equation - 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3

    Note in given question: - 5x^4 + 16x? + 32x= - 6x^4 - 2x^3 considering 2 instead of ?

    Solving:

    - 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3

    - 5x^4 + 16x^2 + 32x+ 6x^4 + 2x^3=0\\- 5x^4+ 6x^4 + 16x^2 + 32x + 2x^3=0\\x^4+2x^3+16x^2+32x=0Taking x common

    x(x^3+2x^2+16x+32)=0\\x=0 \ or \ x^3+2x^2+16x+32=0

    Simplifying \ x^3+2x^2+16x+32=0 \ we \ get (x+2)(x^2+16)

    x=0 \ or \ (x+2)(x^2+16)=0\\x=0 \ or \ x+2=0 \ or x^2+16=0\\x=0 \ or \ x=-2 \ or x^2=-16\\We \ know \ \sqrt{-1}=i \\x=0 \ or \ x=-2 \ or x=\pm 4i\\

    So, the solutions are:

    x=0, x=-2, x=4i, x=-4i

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )