SSC CGL 23 Aug 2021 Shift 2 Paper

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Question : 64 of 100

Marks: +1, -0

If

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

and

x^{2}+x y+y^{2}=3

, then what is the value of

(-x y)

?

$-1$
2
1
$-2$

Solution:

Given,

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

and

x^{2}+y^{2}+x y=3

We can write as

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)

\;\text " and "\;\;x^{2}+y^{2}+x y=3

⇒\;x^{2}+y^{2}=3-x y

Now, Eq. (ii) put in Eq. (i),

⇒ \;\; (3-x y)^{2}-x^{2} y^{2}=21

⇒ 9+x^{2} y^{2}-6 x y-x^{2} y^{2}=21

⇒ \;\; 9-21=6 x y

⇒ \;\; -12=6 x y

⇒ \;\; x y=-2

∴ \;\; (-x y)=-(-2)=2

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