SSC CGL 18 Aug 2021 Shift 2 Paper

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Question : 54 of 100

Marks: +1, -0

If

x^{4}+y^{4}+x^{2} y^{2}=21

and

x^{2}+y^{2}-x y=7

, then what is the value of

\;{x}/{y}+\;{y}/{x}

?

$\;{5}/{4}$
$\;{3}/{4}$
$-\;{3}/{2}$
$-\;{5}/{2}$

Solution:

Given

x^{4}+y^{4}+x^{2} y^{2}=21

and

\;\; x^{2}+y^{2}-x y=7

We can write

x^{4}+y^{4}+2 x^{2} y^{2}-x^{2} y^{2}\;=21

⇒ \;\; (x^{2}+y^{2})^{2}-x^{2} y^{2}=21

. . . (i)

\;{[ ∵ (a+b)^{2}=a^{2}+b^{2}+2 a b]}

. . . (ii)
Put in Eq. (i) we get,

(7+x y)^{2}-x^{2} y^{2} \;\; =21 \;\; . . . \;\text " (iii) "\;

⇒ 49+x^{2} y^{2}+14 x y-x^{2} y^{2} \;\; =21

⇒ \;\; 14 x y=21-49 \;\; =-28

x y \;\; =-2

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

\;\; =\;{(7+x y)}/{x y} \;\; \;\text " [By Eq. (ii)] "\;

\;\; =\;{7-2}/{-2}=-\;{5}/{2}

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