\(x^3-3x^2+3x-1+5x=8\Leftrightarrow\left(x-1\right)^3+5x=8\)
\(y^3-6y^2+12y-8+5y=7\Leftrightarrow\left(y-2\right)^3+5y=7\)
Cộng vế với vế:
\(\Leftrightarrow\left(x-1\right)^3+\left(y-2\right)^3+5\left(x+y-3\right)=0\)
\(\Leftrightarrow\left(x+y-3\right)\left[\left(x-1\right)^2+\left(y-2\right)^2-\left(x-1\right)\left(y-2\right)\right]+5\left(x+y-3\right)=0\)
\(\Leftrightarrow\left(x+y-3\right)\left[\left(x-1-\frac{y-2}{2}\right)^2+\frac{3\left(y-2\right)^2}{4}+5\right]=0\)
\(\Leftrightarrow x+y-3=0\Leftrightarrow x+y=3\)
