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Dragos35
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VA ROG IMI TREBUIE URGENT!! Stiind ca x=√3 si y =1/√3 , aratati ca x/y + y/x = 10/3

Răspuns :


[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]
x= [tex]\sqrt{3}[/tex]

y= [tex]\dfrac{1}{\sqrt{3}}[/tex]= [tex]\dfrac{\sqrt{3}}{3}[/tex]

[tex]\dfrac{x}{y}[/tex]+ [tex]\dfrac{y}{x}[/tex]= [tex]\dfrac{10}{3}[/tex]

[tex]\dfrac{\sqrt{3}}{\frac{\sqrt{3}}{3}}[/tex]+ [tex]\dfrac{\frac{\sqrt{3}}{3}}{\sqrt{3}}[/tex]

[tex]\dfrac{3}{1}[/tex]+ [tex]\dfrac{1}{3}[/tex]= [tex]\dfrac{9+1}{3}[/tex]= [tex]\dfrac{10}{3}[/tex]

Sper să te ajute! ^_^

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