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Math Help - Solving a radical equation

  1. #1
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    Solving a radical equation

    I am not too sure on how to actually solve this radical equation been stuck on it for a while the equation is:

    \sqrt{2x+6} - \sqrt{x+4} =1

    any help would be awesome
    thanks in advance
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by DjNito View Post
    I am not too sure on how to actually solve this radical equation been stuck on it for a while the equation is:

    \sqrt{2x+6} - \sqrt{x+4} =1

    any help would be awesome
    thanks in advance
    I would first rewrite it as \sqrt{2x+6}=1+\sqrt{x+4}.

    Squaring both sides, foiling and simplifying yields: 2x+6=2\sqrt{x+4}+x+5 (Verify)

    Now, get everything but the radical on the other side of the equation: \frac{x+1}{2}=\sqrt{x+4}.

    Square both sides again to get \tfrac{1}{4}(x^2+2x+1)=x+4 \implies x^2-2x-15=0 (Verify)

    Now solve this quadratic equation for x to get two possible answers. Then test for possible extraneous solutions by plugging them into the original equation.

    I hope this helps!
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