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Math Help - Using substitution to solve

  1. #1
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    Using substitution to solve

    I have two problems...

    ({{x+5}\over{x}})^{1\over2}+4({{x}\over{x+5}})^{1\  over2}=4

    \sqrt{3x+4}+\sqrt{x-4}=2\sqrt{x}

    My teacher said substitution is preffered, but I only seem to make it more complicated. If substitution is not possible, solve regularly.

    Can you get me started? Thanks!
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by nathan02079 View Post
    I have two problems...

    ({{x+5}\over{x}})^{1\over2}+4({{x}\over{x+5}})^{1\  over2}=4

    \sqrt{3x+4}+\sqrt{x-4}=2\sqrt{x}

    My teacher said substitution is preffered, but I only seem to make it more complicated. If substitution is not possible, solve regularly.

    Can you get me started? Thanks!
    This should get you started:

    1) Substitute t = \left(\frac{x+5}{x}\right)^{\frac12}  , and you will get a quadratic...

    2) Just try squaring both sides, you will see the magic
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