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Old 2006-10-29, 15:29   #2
victor
 
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Oct 2005
Fribourg, Switzerlan

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Quote:
Originally Posted by fetofs View Post
Could anyone enlighten me with the solution:

Find all integer solutions of the equation x^3-y^3=3(x^2-y^2) and explain why your answer is correct.
\large{x^3-y^3=3(x^2-y^2)}
\large{(x-y)(x^2+x\cdot y+y^2)=3(x+y)(x-y)}
\large{x^2+xy+y^2=3(x+y)}
therefore
\large{x=\frac{sqrt{3-y}sqrt{3(y+1)}-y+3}{2}}
or
\large{x=\frac{-(sqrt{3-y}sqrt{3(y+1)}+y-3)}{2}}

Last fiddled with by victor on 2006-10-29 at 15:29 Reason: thereforE<-
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