# Algebra Problem

• Aug 21st 2012, 07:24 PM
srirahulan
Algebra Problem
If $\displaystyle x+y=a,z+x=2b,y+z=3c$ show that $\displaystyle x^2+y^2+z^2-xy-yz-zx$ show that in terms of a,b,c
• Aug 21st 2012, 07:35 PM
Prove It
Re: Algebra Problem
Quote:

Originally Posted by srirahulan
If $\displaystyle x+y=a,z+x=2b,y+z=3c$ show that $\displaystyle x^2+y^2+z^2-xy-yz-zx$ show that in terms of a,b,c

\displaystyle \displaystyle \begin{align*} x + y \phantom{ + z } &= a \\ x \phantom{ + y} + z &= 2b \\ \phantom{x + } y + z &= 3c \end{align*}

Subtract row 1 from row 2

\displaystyle \displaystyle \begin{align*} x + y \phantom{ +z} &= a \\ \phantom{x} -y + z &= 2b - a \\ \phantom{x + } y + z &= 3c \end{align*}

Add row 2 to row 3

\displaystyle \displaystyle \begin{align*} x + y \phantom{ + z} &= a \\ \phantom{x} -y + z &= 2b - a \\ 2z &= 2b - a + 3c \end{align*}

You should be able to evaluate x, y, z now, and from there solve your problem.
• Aug 21st 2012, 09:10 PM
srirahulan
Re: Algebra Problem
thanks>>><<<