Toán Lớp 8: Tìm x,y thuộc Z:
2x^2 + y^2 – 2xy + 2y – 6x + 5 = 0
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Toán Lớp 8: Tìm x,y thuộc Z:
2x^2 + y^2 – 2xy + 2y – 6x + 5 = 0
Comments ( 1 )
2{x^2} + {y^2} – 2xy + 2y – 6x + 5 = 0\\
\Rightarrow ({x^2} – 4x + 4) + ({x^2} + 2xy + {y^2}) – (2x + 2y) + 1 = 0\\
\Rightarrow {(x – 2)^2} + {(x + y)^2} – 2(x + y) + 1 = 0\\
\Rightarrow {(x – 2)^2} + {(x + y – 1)^2} = 0\\
but\,\,\,{(x – 2)^2} + {(x + y – 1)^2} \ge 0\forall x,y\\
\Rightarrow \left[ \begin{array}{l}
{(x – 2)^2} = 0\\
{(x + y – 1)^2} = 0
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 2\\
y = – 1
\end{array} \right.
\end{array}\]