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3 June, 00:14

Solve x4 - 17x2 + 16 = 0. Let u =

this is a question on my test

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Answers (1)
  1. 3 June, 00:16
    0
    Solve for x over the real numbers:

    x^4 - 17 x^2 + 16 = 0

    Substitute y = x^2:

    y^2 - 17 y + 16 = 0

    The left hand side factors into a product with two terms:

    (y - 16) (y - 1) = 0

    Split into two equations:

    y - 16 = 0 or y - 1 = 0

    Add 16 to both sides:

    y = 16 or y - 1 = 0

    Substitute back for y = x^2:

    x^2 = 16 or y - 1 = 0

    Take the square root of both sides:

    x = 4 or x = - 4 or y - 1 = 0

    Add 1 to both sides:

    x = 4 or x = - 4 or y = 1

    Substitute back for y = x^2:

    x = 4 or x = - 4 or x^2 = 1

    Take the square root of both sides:

    Answer: x = 4 or x = - 4 or x = 1 or x = - 1
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