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Math Help - Problem involving in surd

  1. #1
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    Problem involving in surd

    Please help me to solve this question.
    Find p,

    √189 = √((p-1)^2+20) + √((p-4)^2+80)


    Please help, i don't know how to start off......
    Thanks.
    Last edited by alexander9408; August 12th 2012 at 12:25 AM.
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  2. #2
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    Re: Problem involving in surd

    Hint:

    \sqrt{189} = 3\sqrt{ 21}=\sqrt{21}+2\sqrt{21}=\sqrt{21}+\sqrt{84}
    Thanks from alexander9408
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  3. #3
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    Re: Problem involving in surd

    Quote Originally Posted by alexander9408 View Post
    Please help me to solve this question.
    Find p,

    √189 = √((p-1)^2+20) + √((p-4)^2+80)


    Please help, i don't know how to start off......
    Thanks.
    The gen ral way to do such problems is: square --- islate the square-root --- square --- isolate the square-root ---

    until you have a polynomial equation.

    With your problem:

    Square both sides:

    189 = (p-1)^2+20 + 2\cdot \sqrt{(p-1)^2+20} \cdot \sqrt{(p-4)^2 + 80} + (p-4)^2 + 80

    Expand the brackets and isolate the square-root:

    36-p^2+5p=\sqrt{(p-1)^2+20} \cdot \sqrt{(p-4)^2 + 80}

    Now square again, isolate, ....

    and finally solve the equation. For confirmation only: You should come out with p = 2
    Thanks from alexander9408
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  4. #4
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    Re: Problem involving in surd

    Thank you.
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