Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
\left\{ \begin{array}{l}
{x^2} + {y^2} = 2x\\
{\left( {x - 1} \right)^3} + {y^3} = 2
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left( {{x^2} - 2x + 1} \right) + {y^2} = 1\\
{\left( {x - 1} \right)^3} + {y^3} = 2
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{\left( {x - 1} \right)^2} + {y^2} = 1\\
{\left( {x - 1} \right)^3} + {y^3} = 2
\end{array} \right.\\
a = x - 1 + y;b = \left( {x - 1} \right).y\\
\Rightarrow \left\{ \begin{array}{l}
{a^2} - 2b = 1\\
{a^3} - 3ab = 2
\end{array} \right.\\
{a^2} - 2b = 1 \Rightarrow b = \frac{{{a^2} - 1}}{2}\\
{a^3} - 3ab = 2 \Leftrightarrow {a^3} - 3a.\frac{{{a^2} - 1}}{2} = 2\\
\Leftrightarrow {a^3} - \frac{{3{a^3} - 3a}}{2} = 2\\
\Leftrightarrow 2{a^3} - 3{a^3} + 3a = 4\\
\Leftrightarrow - {a^3} + 3a - 4 = 0
\end{array}\]
