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SSC Selection Post 2022 PYQ — Question 73

SSC Selection Post - Graduation Level - 8 Feb 2022 - Shift 3 • Quantitative Aptitude • Q73

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If x4 + y4 + x2y2 = 21 and x2 + y2 - xy = 7, then what is the value of 1x2{1 \over x^2} + 1y2{1 \over y^2}.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 54{5 \over 4}.

x4 + y4 + x2y2 = (x2 + y2 - xy)(x2 + y2 + xy)

⇒ 21 = 7(x2 + y2 + xy)

⇒ (x2 + y2 + xy) = 3   .....(1)

Also, x2 + y2 - xy = 7   .....(2)

From (1) and (2), 2xy = - 4

⇒ xy = - 2

⇒ (xy)2 = 4

From equation (2), x2 + y2 = 7 - 2 = 5

Now, (1/x2 + 1/y2) = (x2 + y2)/(xy)2 = 5/4