Question

VA ROG IMI TREBUIE URGENT!! Stiind ca x=√3 si y =1/√3 , aratati ca x/y + y/x = 10/3

Answer 1

[tex]\it xy=\sqrt3\cdot\dfrac{1}{\sqrt3} = \dfrac{\sqrt3}{\sqrt3} =1 \ \ \ \ (*) \\\;\\ \\\;\\ \dfrac{^{x)}x}{\ y} + \dfrac{^{y)}y}{\ x} = \dfrac{x^2+y^2}{xy} \stackrel{(*)}{=} x^2+y^2 = (\sqrt3)^2+\left(\dfrac{1}{\sqrt3}\right)^2=3+\dfrac{1}{3} [/tex]

Answer 2

x= $\sqrt{3}$

y= $\dfrac{1}{\sqrt{3}}$= $\dfrac{\sqrt{3}}{3}$

$\dfrac{x}{y}$+ $\dfrac{y}{x}$= $\dfrac{10}{3}$

$\dfrac{\sqrt{3}}{\frac{\sqrt{3}}{3}}$+ $\dfrac{\frac{\sqrt{3}}{3}}{\sqrt{3}}$

$\dfrac{3}{1}$+ $\dfrac{1}{3}$= $\dfrac{9+1}{3}$= $\dfrac{10}{3}$

Sper să te ajute! ^_^