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Math Help - Algebraic Equation ヽ(□`。)ノ Need help~

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    Algebraic Equation ヽ(□`。)ノ Need help~

    Given that 81h/2e + 2e/h = 18,
    Find the value of e : h

    Does anyone here know how I should go about doing this? I confused myself mid-way when attempting to solve the equation >n<;
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Quote Originally Posted by asterism View Post
    Given that 81h/2e + 2e/h = 18,
    Find the value of e : h

    Does anyone here know how I should go about doing this? I confused myself mid-way when attempting to solve the equation >n<;
    Assuming this is \displaystyle \begin{align*} \frac{81h}{2e} + \frac{2e}{h} = 18 \end{align*}, then

    \displaystyle \begin{align*} h \left(\frac{81h}{2e} + \frac{2e}{h} \right) &= 18h \\ \frac{81}{2e}h^2 + 2e &= 18h \\ \frac{81}{2e}h^2 - 18h + 2e &= 0 \end{align*}

    And now solve for h using the Quadratic Formula.
    Last edited by Prove It; October 9th 2012 at 02:09 AM.
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Quote Originally Posted by Prove It View Post
    Assuming this is \displaystyle \begin{align*} \frac{81h}{2e} + \frac{2e}{h} = 18 \end{align*}, then

    \displaystyle \begin{align*} h \left(\frac{81h}{2e} + \frac{2e}{h} \right) &= 18h \\ \frac{81}{2e}h^2 + 2e &= 18h \\ \frac{81}{2e}h^2 - 18h + 2e &= 0 \end{align*}

    And now solve for h using the Quadratic Formula.
    Instead of solving \frac{81}{2e}h^2 - 18h + 2e = 0 for h and then dividing e by that h, you could divide both sides by e to get \frac{81}{2}\left(\frac{h}{e}\right)^2 - 18\frac{h}{e} + 2 = 0 and solve it to find \frac{h}{e}. This can also be done starting from the initial equation \frac{81h}{2e} + \frac{2e}{h} = 18. If we denote e / h by x, then the equation becomes \frac{81}{2}\frac{1}{x} + 2x = 18, which turns into a quadratic equation in x after multiplying by x.
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Thank you. >//v//<"

    But I have another question: which method should I use in solving the quadratic equation? Factorization or?
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Quote Originally Posted by asterism View Post
    Thank you. >//v//<"

    But I have another question: which method should I use in solving the quadratic equation? Factorization or?
    I doubt it factorises. Use the Quadratic Formula.
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Okay!!
    I haven't learnt it in class yet but I'll google it.

    Also, I really like your signature. xD;
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Quote Originally Posted by asterism View Post
    I haven't learnt it in class yet but I'll google it.
    When I was in a freshman in high school, I took part in a math competition designed for sophomores. There was a quadratic equation, and I could not solve it because we had not covered the quadratic formula yet though I believe we had covered completing the square. Later my math teacher told me that I could have derived the quadratic formula by completing the square. So don't be afraid to study the quadratic formula and how to derive it. I personally never use factorization but instead apply the quadratic formula.
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    Re: Algebraic Equation ヽ(□`。)ノ Need help~

    Quote Originally Posted by asterism View Post
    Given that 81h/(2e) + 2e/h = 18
    I try to use LCD where easiest:

    81h/(2e) = 18 - 2e/h
    81h/(2e) = (18h - 2e)/h
    Criss-cross multiplication:
    81h^2 = 36eh - 4e^2

    81h^2 - 36eh + 4e^2 = 0
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