Question

СРОЧНО ДАМ 60 БАЛЛОВ ЗА РЕШЕНИЕ С ОБЪЯСНЕНИЕМ.
Система уравнений

Answer 1

$\displaystyle\bf\\\left \{ {\dfrac{1}{x}+\dfrac{1}{y} =5 } \atop {\dfrac{1}{x^{2} }+\dfrac{1}{y^{2} }=13 }} \right. \\\\\\\left \{ {{\dfrac{x+y}{xy} }=5 \atop {\dfrac{x^{2}+y^{2} }{x^{2} y^{2} }=13}} \right.\\\\\\\left \{ {{x+y=5xy} \atop {x^{2} +y^{2} }=13x^{2} y^{2} } \right. \\\\\\ \left \{ {{x+y=5xy} \atop {(x+y)^{2} }-2xy=13x^{2} y^{2} } \right. \\\\\\\left \{ {{x+y=5xy} \atop {25x^{2} y^{2} -2xy=13x^{2} y^{2} }} \right.\\\\\\12x^{2} y^{2}-2xy=0\\\\2xy\cdot(6xy-1)=0$

$\displaystyle\bf\\xy\neq 0\\\\6xy-1=0\\\\6xy=1\\\\xy=\frac{1}{6} \\\\Otvet \ : \ A$