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Albert
Well-known member
- Jan 25, 2013
- 1,225
x,y are integers and
$x^2-xy+2y^2=116$
find max(xy) and min(xy)
$x^2-xy+2y^2=116$
find max(xy) and min(xy)
yes, it could be solved to use a more analytical solution,try it ! it is not hard !I rewrote the problem with $w=xy \Rightarrow y=\frac w x$ to get:
$x^2-w+2\frac {w^2} {x^2}=116$
Feeding it to Wolfram gives a nice graph and all 12 integer solutions, with the minimum of -30 and the maximum of 63.
Likewise, it would be nice to see a more analytical solution.