\(\Leftrightarrow3x^2+6xy+14y^2+7xy=330\Leftrightarrow3x\left(x+2y\right)+7y\left(x+2y\right)=330\)
\(\Leftrightarrow\left(x+2y\right)\left(3x+7y\right)=330\)
\(\Leftrightarrow\left(x+2y\right)\left(3x+7y\right)=330.1=165.2=10.33=5.66=15.22\)
x,y nguyên dương => 3x+7y > x+3y>2
TH1: \(\left\{{}\begin{matrix}x+2y=10\\3x+7y=33\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=3\end{matrix}\right.\left(n\right)\)
TH2: \(\left\{{}\begin{matrix}x+2y=5\\3x+7y=66\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-97\\y=51\end{matrix}\right.\left(l\right)\)
TH3:\(\left\{{}\begin{matrix}x+2y=15\\3x+7y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=61\\y=-23\end{matrix}\right.\) (l)
\(\Rightarrow x=4;y=3\)
Ta có : 3x^2+14y^2+13xy=330
(=) x2 +14/3y2+13/3xy=110
(=) x2+2.13/6xy+169/36y2-169/36y2+14/3y2=110
=> (x+13/6y)2 -1/36y^2=110
(=) (x+13/6y-1/6y)(x+13/6y+1/6y)=110
=)(x+2y)(x+7/3y)=2.5.11=10.11=11.10=22.5=5.22=55.2=2.55
=> x=4;y=3