[latex] \left \{ {{ \frac{1}{x} + \frac{1}{y} = \frac{3}{2} } \atop { \frac{1}{ x^{2} }+ \frac{1}{y^{2} } = \frac{5}{4} }} \right. [/latex]надо решить систему уравнений

[latex] \left \{ {{ \frac{1}{x} + \frac{1}{y} = \frac{3}{2} } \atop { \frac{1}{ x^{2} }+ \frac{1}{y^{2} } = \frac{5}{4} }} \right. \\\ \frac{1}{x}=a \\\ \frac{1}{y}=b \\\ \left \{ {{ a+b = 1.5 } \atop { a^2+ b^2 =1.25 }} \right. \\\ a=1.5-b \\\ (1.5-b)^2+b^2=1.25 \\\ 2b^2-3b+1=0 \\\ D=9-8=1 \\\ b_1= \frac{3+1}{4}=1 \\\ b_2= \frac{3-1}{4}=0.5 \\\ a_1=1.5-1=0.5 \\\ a_2=1.5-0.5=1[/latex] [latex]x=\frac{1}{a} \\\ x_1=\frac{1}{0.5}=2 \\\ x_2=\frac{1}{1}=1 \\\ y= \frac{1}{b} \\\ y_1=\frac{1}{1}=1 \\\ y_2=\frac{1}{0.5}=2[/latex] Ответ: (2; 1); (1; 2)