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  1. #1
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    Algebra

    Solve for $\displaystyle m$
    $\displaystyle 5m^4+24m^2-36=0\;m^2=y\Rightarrow 5y^2+24y-36=0$
    Then i plugged it into the quadratic formula
    $\displaystyle y=\frac{-24\pm\sqrt{24^2-(4)(5)(-36)}}{10}\Rightarrow y=\frac{-24\pm36}{10}\;y=\frac{6}{5}\;y=-6$
    From there i did $\displaystyle m^2=\frac{6}{5}\Rightarrow m=\pm\sqrt\frac{6}{5}$
    $\displaystyle m^2=-6$ Which gives an imaginary answer, so I really cant use that as answer right?

    P.S. I used $\displaystyle m=\pm\sqrt\frac{6}{5}$ as my answer and I got marked off 1 point anyone know why?
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  2. #2
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    That's good, subbing y for m^2. Therefore, you get a quadratic.

    Just factor it.

    $\displaystyle 5y^{2}+24y-36=0$

    $\displaystyle (y+6)(5y-6)=0$

    Now, sub m^2 back in:

    $\displaystyle (m^{2}+6)(5m^{2}-6)=0$

    Now, The M^2+6 results in 2 non-real solutions.

    The 5m^2-6 will give two real solutions.
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  3. #3
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    Do you think I should put the non real answers as well as the real answers on my test as the answers for what m equals?
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  4. #4
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    Hello, OzzMan!

    Solve for $\displaystyle m$

    $\displaystyle 5m^4+24m^2-36\:=\:0$

    Let $\displaystyle m^2\,=\,y\quad\Rightarrow\quad 5y^2+24y-36\:=\:0$

    Then i plugged it into the quadratic formula:

    $\displaystyle y\:=\:\frac{-24\pm\sqrt{24^2-(4)(5)(-36)}}{10}\quad\Rightarrow\quad y\:=\:\frac{-24\pm36}{10} \;=\;\frac{6}{5}\;-6$


    From there i did $\displaystyle m^2\:=\:\frac{6}{5}\quad\Rightarrow\quad m\:=\:\pm\sqrt\frac{6}{5}$

    $\displaystyle m^2\:=\:-6$ which gives an imaginary answer.


    P.S. I used $\displaystyle m\:=\:\pm\sqrt\frac{6}{5}$ as my answer and I got marked off 1 point.
    Anyone know why?

    Just a guess . . . maybe you were expected to rationalize that square root?

    . . $\displaystyle \pm\sqrt{\frac{6}{5}} \;=\;\pm\sqrt{\frac{6}{5}\cdot\frac{5}{5}} \;=\;\pm\sqrt{\frac{30}{25}} \;=\;\pm\frac{\sqrt{30}}{\sqrt{25}} \;=\;\pm\frac{\sqrt{30}}{5} $


    Oh yes, your reasoning and your work is correct . . . Nice going!

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  5. #5
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    oh that makes a lot of sense thanks
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