[tex] \left \{ {{ \frac{1}{x} + \frac{1}{y}= \frac{3}{2} } \atop { \frac{1}{ x^{2} }+ \frac{1}{ y^{2} }= \frac{5}{4} }} ight. [/tex]

(1/x+1/y)²=1/x²+1/y²+2/xy1/x+1/y=3/5⇒(1/x+1/y)²=9/41/x²+1/y²=5/45/4+2/xy=9/42/xy=9/4-5/42/xy=1xy=2x=2/yy/2+1/y=3/2y²+2=3yy²-3y+2=0y1+y2=3 U y1*y2=2y1=1⇒x1=2/1=2y2=2⇒x2=2/2=1(2;1);(1;2)