Question

Știind că x=√3 si y =1/√3 , arătați că x/y+y/x=10/3

Answer 1

x=√3 si y =1/√3
x/y+y/x=10/3                                          /*3
√3/1/√3+1/√3/√3=√3*√3+1/√3*1/√3=3+1/3= (9+1) /3=10/3

Answer 2

$\displaystyle x= \sqrt{3} ;~y= \frac{1}{ \sqrt{3} } ,~ \frac{x}{y} + \frac{y}{x} = \frac{10}{3} \\ --------------- \\ \frac{ \sqrt{3} }{ \frac{1}{ \sqrt{3} } } + \frac{ \frac{1}{ \sqrt{3} } }{ \sqrt{3} } = \sqrt{3} : \frac{1}{ \sqrt{3} }+ \frac{1}{ \sqrt{3} } : \sqrt{3} = \sqrt{3} \cdot \sqrt{3} + \frac{1}{ \sqrt{3} } \cdot \frac{1}{ \sqrt{3} } = \\ =3+ \frac{1}{3} = \frac{3 \cdot 3+1}{3} = \frac{9+1}{3} = \frac{10}{3}$