College Algebra help!!!

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I have to solve each equation using a u substitution and need help understanding how to do this.

The first equation is:
1. x^2/3-2x^1/3-15=0

2. x+4=7 Squareroot x+4

  • College Algebra help!!! -

    x^2/3-2x^1/3-15=0
    (x^(1/3))^2 - 2x^(1/3) - 15 = 0
    suppose we let x^(1/3) = y, then we get

    y^2 - 2y - 15 = 0
    (y-5)(x+3) = 0
    y = 5 or y = -3

    then x^(1/3)= 5 , cube both sides
    x = 125
    or
    x^(1/3) = -3
    x = -27

    2.
    x+4 = 7√(x+4)
    square both sides
    x^2 + 8x + 16 = 49(x+4)
    x^2 + 8x + 16 = 49x +196
    x^2 - 41x - 180=0
    (x-45)(x+4) = 0
    x = 45 or x = -4

    BUT, since we squared, we must verify all answers
    if x = 45
    LS = 45+4 = 49
    RS = 7√49 = 49 , works

    if x = -4
    LS = 0
    RS = 7√0 = 0 , works

    so x = 45 or x = -4

  • College Algebra help!!! -

    Thank you so much this makes the examples provided make much more scense the way you broke them down! Thanks!

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