Toán Lớp 8: Tìm x. x2 – 4xy + 5y2 – 22y + 10x +28 =0
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Toán Lớp 8: Tìm x. x2 – 4xy + 5y2 – 22y + 10x +28 =0
Comments ( 1 )
{x^2} – 4xy + 5{y^2} – 22y + 10x + 28 = 0\\
\Leftrightarrow \left( {{x^2} – 4xy + 4{y^2}} \right) + \left( {10x – 20y} \right) + \left( {{y^2} – 2y + 1} \right) + 27 = 0\\
\Leftrightarrow \left[ {{x^2} – 2.x.2y + {{\left( {2y} \right)}^2}} \right] + 10\left( {x – 2y} \right) + \left( {{y^2} – 2.y.1 + {1^2}} \right) + 27 = 0\\
\Leftrightarrow {\left( {x – 2y} \right)^2} + 10.\left( {x – 2y} \right) + {\left( {y – 1} \right)^2} + 27 = 0\\
\Leftrightarrow \left[ {{{\left( {x – 2y} \right)}^2} + 10\left( {x – 2y} \right) + 25} \right] + {\left( {y – 1} \right)^2} + 2 = 0\\
\Leftrightarrow \left[ {{{\left( {x – 2y} \right)}^2} + 2.\left( {x – 2y} \right).5 + {5^2}} \right] + {\left( {y – 1} \right)^2} + 2 = 0\\
\Leftrightarrow {\left[ {\left( {x – 2y} \right) + 5} \right]^2} + {\left( {y – 1} \right)^2} + 2 = 0\\
\Leftrightarrow {\left( {x – 2y + 5} \right)^2} + {\left( {y – 1} \right)^2} + 2 = 0\\
{\left( {x – 2y + 5} \right)^2} \ge 0,\,\,\,\forall x,y\\
{\left( {y – 1} \right)^2} \ge 0,\,\,\,\forall y\\
\Rightarrow {\left( {x – 2y + 5} \right)^2} + {\left( {y – 1} \right)^2} + 2 \ge 2 > 0,\,\,\,\forall x,y\\
\Rightarrow Phương\,\,trình\,\,vô\,\,nghiệm
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