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Math Help - 2 Algebraic Equations

  1. #1
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    2 Algebraic Equations

    I've been stuck on these two. If you could help me and show the work. Thanks.

    8-sqrt(y-1)=6



    x^2/3-10x^1/3+9=0
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  2. #2
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    If someone could help I'd be very grateful. Thanks.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Nash55 View Post
    I've been stuck on these two. If you could help me and show the work. Thanks.

    8-sqrt(y-1)=6
    8 - \sqrt{y - 1} = 6

    \Rightarrow - \sqrt {y - 1} = -2

    now, square both sides and continue


    x^2/3-10x^1/3+9=0
    note that we have
    \left( x^{1/3} \right)^2 - 10 \left( x^{1/3} \right) + 9 = 0

    this is quadratic in x^{1/3}. this becomes as clear as day if we say let x^{1/3} = y, then we get

    y^2 - 10y + 9 = 0

    now solve for y. when done, replace y with x^{1/3} and then solve for x
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