- #1
anemone
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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Prove that if $\dfrac{a+b}{3x-y}=\dfrac{b+c}{3y-z}=\dfrac{c+a}{3z-x}$, then $\dfrac{a+b+c}{x+y+z}=\dfrac{ax+by+cz}{x^2+y^2+z^2}$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Prove that if $\dfrac{a+b}{3x-y}=\dfrac{b+c}{3y-z}=\dfrac{c+a}{3z-x}$, then $\dfrac{a+b+c}{x+y+z}=\dfrac{ax+by+cz}{x^2+y^2+z^2}$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!