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Algebra2

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Rational Exponet Equations:
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1.(x^2+9x+22)^3/2 = 8

2.(5x-5)^2/3 = 16

  • Algebra2 - ,

    1.
    raise both sides to the 2/3 , notice that 2/3 is the reciprocal of 3/2

    [ (x^2 + 9x + 22)^(3/2) ] ^(2/3) = 8^(2/3)
    (x^2 + 9x + 22)^1 = 8^(2/3)

    x^2+9x+22 = 4
    x^2 + 9x + 18 = 0
    (x+6)(x+3) = 0
    x = -6 or x = -3

    Since we effectively squared both sides, ( ^(2/3) is the same as taking the cube root, then squaring), all answers must be verified.

    if x = -6
    LS = (36 - 54 + 22)^(3/2
    = 4^(3/2) = 8
    = RS

    if x=-3
    LS = (9-27+22)^(3/2)
    = 4^(3/2) = 8
    = RS

    so x=-6 or x=-3

    You try the second one in the same way.

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