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Math Help - factorising quadratic formulas

  1. #1
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    Post factorising quadratic formulas

    Im having trouble factorising:

    (x/(16 + x)^) - 1/3 = 0

    Thats the square root of (16+x*x) divided by x, minus 1/3. I have to find the values that make it equal 0.
    Can someone please help me?
    Thanks!
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  2. #2
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    Quote Originally Posted by pleasehelpme View Post
    Im having trouble factorising:

    (x/(16 + x )^) - 1/3 = 0

    Thats the square root of (16+x*x) divided by x, minus 1/3. I have to find the values that make it equal 0.
    Can someone please help me?
    Thanks!
    \frac{x}{\sqrt{16 + x^2}} - \frac{1}{3} = 0 \Rightarrow x = \frac{\sqrt{16 + x^2}}{3} \Rightarrow x^2 = \frac{16 + x^2}{9} \Rightarrow 9x^2 = 16 + x^2

    and the coup de grace is left for you.
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  3. #3
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    How did you get the equation over 9 in step 3? and how did you get the equation to equal x-squared?
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  4. #4
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    Quote Originally Posted by pleasehelpme View Post
    How did you get the equation over 9 in step 3? and how did you get the equation to equal x-squared?
    Mr F edits:

    Quote Originally Posted by mr fantastic View Post
    \frac{x}{\sqrt{16 + x^2}} - \frac{1}{3} = 0


    {\color{red}\Rightarrow \frac{x}{\sqrt{16 + x^2}} = \frac{1}{3}}


    Multiply both sides by {\color{red}\sqrt{16 + x^2}}:



    \Rightarrow x = \frac{\sqrt{16 + x^2}}{3}


    Square both sides:


    \Rightarrow x^2 = \frac{16 + x^2}{9} \Rightarrow 9x^2 = 16 + x^2

    and the coup de grace is left for you.
    If you're attempting these sorts of questions you're expected to be comfortable with this sort of algebraic manipulation.
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