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9 March, 01:33

Find one value of x that is a solution to the equation:

(x^2 - 8) ^2 + x^2 - 8 = 20

x=

+2
Answers (1)
  1. 9 March, 01:49
    0
    x = 2 sqrt (3) or x = - 2 sqrt (3) or x = sqrt (3) or x = - sqrt (3)

    Step-by-step explanation:

    Solve for x:

    -8 + x^2 + (x^2 - 8) ^2 = 20

    Expand out terms of the left hand side:

    x^4 - 15 x^2 + 56 = 20

    Subtract 20 from both sides:

    x^4 - 15 x^2 + 36 = 0

    Substitute y = x^2:

    y^2 - 15 y + 36 = 0

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

    (y - 12) (y - 3) = 0

    Split into two equations:

    y - 12 = 0 or y - 3 = 0

    Add 12 to both sides:

    y = 12 or y - 3 = 0

    Substitute back for y = x^2:

    x^2 = 12 or y - 3 = 0

    Take the square root of both sides:

    x = 2 sqrt (3) or x = - 2 sqrt (3) or y - 3 = 0

    Add 3 to both sides:

    x = 2 sqrt (3) or x = - 2 sqrt (3) or y = 3

    Substitute back for y = x^2:

    x = 2 sqrt (3) or x = - 2 sqrt (3) or x^2 = 3

    Take the square root of both sides:

    Answer: x = 2 sqrt (3) or x = - 2 sqrt (3) or x = sqrt (3) or x = - sqrt (3)
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