Weird Basic Algebra Problem (Help Appreciated =D )

FIRESSS · January 19th 2007, 12:02 AM

Hello,

I got this annoying problem I can't seem to get around, I know there's a trick somewhere in the book for this...I think there is, anyhow, I need to solve the following equation for x:

(s^2 - 2sx + x^2)(a) = (x^2)(b)

Each time I try to mess around with x and s, I'm unable to break the 2sx term and it's rly getting to me, at my last step I got to this useless mess:

(s^2 - 2sx)/(x^2) = (b/a)(x^2)

Any tips/tricks highly appreciated, spanks!

**earboth** · January 19th 2007, 12:17 AM

Originally Posted by FIRESSS

Hello,

I got this annoying problem I can't seem to get around, I know there's a trick somewhere in the book for this...I think there is, anyhow, I need to solve the following equation for x:

(s^2 - 2sx + x^2)(a) = (x^2)(b)

Each time I try to mess around with x and s, I'm unable to break the 2sx term and it's rly getting to me, at my last step I got to this useless mess:

(s^2 - 2sx)/(x^2) = (b/a)(x^2)

Any tips/tricks highly appreciated, spanks!

Hello,

if you factorize the first bracket you'll notice that it is a complete square: $s^2-2sx+x^2=(s-x)^2$

After a few steps you'll get the proportion:

$\frac{(s-x)^2}{x^2}=\frac{a}{b} \Longleftrightarrow \left( \frac{s-x}{x} \right)^2=\frac{a}{b}$

EB

**Soroban** · January 19th 2007, 06:02 AM

Hello, FIRESSS!

Solve for $x:\;\;a(s^2-2sx+x^2)\;=\;bx^2$

Why not expand it and solve the resulting quadratic equation?

We have: . $as^2 -2asx + ax^2\;=\;bx^2\quad\Rightarrow\quad(a-b)x^2 - 2asx + as^2\;=\;0$

Quadratic Formula: . $x \;=\;\frac{-(\text{-}2as) \pm \sqrt{(\text{-}2as)^2 - 4(a-b)(as^2)}}{2(a-b)}$

. . which simplifies to: . $x \;=\;\frac{as \pm s\sqrt{ab}}{a-b}$

Thread: Weird Basic Algebra Problem (Help Appreciated =D )

LinkBack

Thread Tools

Display

Weird Basic Algebra Problem (Help Appreciated =D )

Similar Math Help Forum Discussions

Basic Algebra Problem - Is there a better way of solving this?

Weird basic question

Algebra in geometry problem...help much appreciated

need help with basic algebra problem

weird algebra problem

Search Tags