# Thread: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

1. ## 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<;

2. ## Re: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

Originally Posted by asterism
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 \displaystyle \begin{align*} \frac{81h}{2e} + \frac{2e}{h} = 18 \end{align*}, then

\displaystyle \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.

3. ## Re: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

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

\displaystyle \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 $\displaystyle \frac{81}{2e}h^2 - 18h + 2e = 0$ for h and then dividing e by that h, you could divide both sides by e to get $\displaystyle \frac{81}{2}\left(\frac{h}{e}\right)^2 - 18\frac{h}{e} + 2 = 0$ and solve it to find $\displaystyle \frac{h}{e}$. This can also be done starting from the initial equation $\displaystyle \frac{81h}{2e} + \frac{2e}{h} = 18$. If we denote e / h by x, then the equation becomes $\displaystyle \frac{81}{2}\frac{1}{x} + 2x = 18$, which turns into a quadratic equation in x after multiplying by x.

4. ## 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?

5. ## Re: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

Originally Posted by asterism
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.

6. ## 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;

7. ## Re: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

Originally Posted by asterism
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.

8. ## Re: Algebraic Equation ヽ(´□｀。)ﾉ Need help~

Originally Posted by asterism
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