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STRAIGHT LINE

Posted January 24th, 2010 by magaski0000
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If the equations $ (q-r)x+(r-p)y+(p-q)=0 $ and $ (q^3-r^3)x+(r^3-p^3)y+(p^3-q^3)=0 $ represent the same line, then prove that either p=q or q=r or p+q+r=0

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Comments

answer

On January 24th, 2010 Structure says:

Lines ax+by+c=0 and Ax+By+C=0 are the same if and only if
$ bC-cB=0 $ $ cA-aC=0 $ and $ aB-bA=0 $
In your case you must have three equations , one of them looks

$$(q-r)(r^3-p^3)-(r-p)(q^3-r^3)=0$$
$$(q-r)(r-p)(r^2+rp+p^2)-(r-p)(q-r)(q^2+qr+r^2)=0$$
$$(q-r)(r-p)(p^2-q^2+r(p-q))=0$$
$$(q-r)(r-p)(p-q)(p+q+r)=0$$

THANK YOU

On January 25th, 2010 magaski0000 says:

$ \tau\hbar\alpha\eta\kappa \Upsilon\o\mu $

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