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22 June, 10:26

Solve issuing quadratic techniques

x^4 - 29x^2 + 100 = 0

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Answers (1)
  1. 22 June, 13:03
    0
    Define y = x².

    Then the given equation may be written as

    y² - 29y + 100 = 0

    Factorize to obtain

    (y - 4) (y - 25) = 0

    The solutions are

    y = 4 or y = 25

    Because y = x², obtain

    x² = 4 = > x = 2 or x = - 2.

    x² = 25 = > x = 5 or x = - 5

    The solution for x is 2, - 2, 5, - 5.

    A plot of the function (shown below) verifies that the answer is correct.

    Answer: x = 2, - 2, 5, - 5
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