Question

Решите систему уравнений

Answer 1

$\left \{ {{\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{5}{2}} \atop {x+y=10}} \right. \; ,\; x\ne 0\; ,\; y\ne 0\\\\t=\sqrt{\frac{x}{y}}\; ,\; \left \{ {{t+\frac{1}{t}=\frac{5}{2}} \atop {x+y=10}} \right. \; ,\; \left \{ {{2t^2-5t+2=0,\; t\ne 0} \atop {x+y=10}} \right. \; ,\; \left \{ {{t=\frac{1}{2},\; t=2} \atop {x+y=10}} \right. \\\\\sqrt{\frac{x}{y}}=\frac{1}{2}\; ,\; \frac{x}{y}=\frac{1}{4}\; ,\; y=4x\\\\\sqrt{\frac{x}{y}}=2\; ,\; \frac{x}{y}=4\; ,\; x=4y$

$a)\; \; \left \{ {{y=4x} \atop {x+y=10}} \right. \; ,\; \left \{ {{y=4x} \atop {5x=10}} \right. \; ,\; \left \{ {{y=8} \atop {x=2}} \right. \\\\b)\; \; \left \{ {{x=4y} \atop {x+y=10}} \right. \; ,\; \left \{ {{x=4y} \atop {5y=2}} \right. \; ,\; \left \{ {{x=8} \atop {y=2}} \right. \\\\Otvet:\; \; (2,8)\; ,\; (8,2)\; .$