Question

\(\left\{{}\begin{matrix}x^3+3xy^2=-49\\x^2-8xy+y^2=8y-17x\end{matrix}\right.\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}x^3+3xy^2=-49\\3x^2-24xy+3y^2=24y-51x\end{matrix}\right.\)

Cộng vế:

\(x^3+3x^2+3y^2\left(x+1\right)-24y\left(x+1\right)+51x+49=0\)

\(\Leftrightarrow\left(x+1\right)^3+3y^2\left(x+1\right)-24y\left(x+1\right)+48\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)^3+3\left(x+1\right)\left(y-4\right)^2=0\)

\(\Leftrightarrow\left(x+1\right)\left[\left(x+1\right)^2+3\left(y-2\right)^2\right]=0\)