\(x^2+2y^2+3xy+8=9x+10y\)
\(\Leftrightarrow4x^2+8y^2+12xy+32-36x-40y=0\)
\(\Leftrightarrow4x^2+12x\left(y-3\right)+\left(8y^2-40y+32\right)=0\)
\(\Leftrightarrow4x^2+12x\left(y-3\right)+9\left(y-3\right)^2-\left(y^2-14y+49\right)=0\)
\(\Leftrightarrow\left[2x-3\left(y-3\right)\right]^2-\left(y-7\right)^2=0\)
\(\Leftrightarrow\left[2x-3\left(y-3\right)-\left(y-7\right)\right].\left[2x-3\left(y-3\right)+\left(y-7\right)\right]=0\)
\(\Leftrightarrow\left(2x-4y+16\right)\left(2x-2y+2\right)=0\)
\(\Leftrightarrow\left(x-2y+8\right)\left(x-y+1\right)=0\)
-TH1: \(x-2y+8=0\) \(\Leftrightarrow x=2y-8\) thay vào pt đề cho tìm được x, y.
Tương tự cho TH2
