1. ## Algebra Problem

If $x+y=a,z+x=2b,y+z=3c$ show that $x^2+y^2+z^2-xy-yz-zx$ show that in terms of a,b,c

2. ## Re: Algebra Problem

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

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