Question

$left { {{ frac{1}{x} + frac{1}{y}= frac{3}{2} } atop { frac{1}{ x^{2} }+ frac{1}{ y^{2} }= frac{5}{4} }} right.$

Answer 1

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