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Math Help - Find all real solutions

  1. #1
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    Post Find all real solutions

    Hi! I am studying for a final and have gotten stuck (over & over again!)
    On this certain problem, I am supposed to find all real solutions for the square root of x + 3 + the square root of x + 8= 1
    So far, I have done...
    square root of x + 3 = 1 - the square root of x + 8
    (square root of x + 3 )^2= (1 - the square root of x + 8)^2

    And, I'm not really sure where to go from here. Any help would be greatly appreciated!

    Thanks,
    Ashley
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by aperkin2 View Post
    Hi! I am studying for a final and have gotten stuck (over & over again!)
    On this certain problem, I am supposed to find all real solutions for the square root of x + 3 + the square root of x + 8= 1
    So far, I have done...
    square root of x + 3 = 1 - the square root of x + 8
    (square root of x + 3 )^2= (1 - the square root of x + 8)^2

    And, I'm not really sure where to go from here. Any help would be greatly appreciated!

    Thanks,
    Ashley
    From there, expand and simplify:

    \left(\sqrt{x+3}\right)^2=\left(1-\sqrt{x+8}\right)^2\implies x+3=1-2\sqrt{x+8}+x+8 \implies 2\sqrt{x+8}=6\implies \sqrt{x+8}=3\implies x=1

    But when you plug in x=1 into the expression, you end up with \sqrt{4}+\sqrt{9}=1\implies 5=1 which is impossible. Therefore, there is no real solution.

    Does this make sense?
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  3. #3
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    Hi! I do understand your answer. I didn't know that (1 - the square root of x + 8)^2 would give me 1-2 the square root of x + 8) + x+ 8. I am sure a lot of my problems stem from having trouble with the basics. Thank you so much for your help!

    Ashley
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