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28 August, 11:55

What are the solutions of the equation x^4 + 95x^2 - 500 = 0? Use factoring to solve

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  1. 28 August, 11:57
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    1) given x^4 + 95x^2 - 500

    2) split in two factors with common factor term x^2: (x^2 + ) (x^2 - )

    3) find two numbers that add up 95 and their product is - 500:

    => 100 * (-5) = - 500 and 100 - 5 = 95

    => (x^2 + 100) (x^2 - 5)

    4) factor x^2 - 5 = (x + √5) (x - √5)

    5) write the prime factors: (x^2 + 100) (x + √5) (x - √5)

    6) find the solutions:

    x^2 + 100 = 0 = > not possible

    x + √5 = 0 = > x = - √5

    x - √5 = 0 = > x = √5

    Answer: x = √5 and x = - √5
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