If x+y=3 and \frac{1}{x}+\frac{1}{y}=-\frac{3}{10}, then the value of (x^{2}{ }^{x} y^{2} y_{\text{is }}

SSC CGL 18 Aug 2021 Shift 2 Paper

Question : 63 of 100

Marks: +1, -0

x+y=3

and

\;{1}/{x}+\;{1}/{y}=-\;{3}/{10}

, then the value of

(x^{2}{ }^{x} y^{2} y_{\;\text "is "\;}

Solution:

Given,

x+y=3

and

\;{1}/{x}+\;{1}/{y}=-\;{3}/{10}

⇒ \;\; \;{(x+y)}/{x y}=-\;{3}/{10}

We know that,

\;(x+y)^{2}=x^{2}+y^{2}+2 x y

\;\text " Here, "\;\;x+y=3, x y=-10

\;\text " So, "\; \;\; (3)^{2}=x^{2}+y^{2}+2(-10)

⇒\;9=x^{2}+y^{2}-20

∴ \;x^{2}+y^{2}=29

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