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SSC Selection Post 2022 PYQ — Question 71

SSC Selection Post - Matriculation Level 2022 - 9 Feb 2022 - Shift 1 • Quantitative Aptitude • Q71

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If xy+yx=1{{x\over y} + {y\over x}} = 1 and x, y ≠ 0, then find the value of x6+y6+2x3y3x ^ 6 + y ^ 6 + 2x ^ 3 y ^ 3.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 0.

xy+yx=1{{x\over y} + {y\over x}} = 1

⇒ x2+y2xy=1{{x^2+y^2\over xy}}= 1

⇒ x2 + y2 - xy = 0

⇒ x6+y6+2x3y3x ^ 6 + y ^ 6 + 2x ^ 3 y ^ 3 = (x3 + y3)2

⇒ ((x + y)(x2 + y2 - xy))2 = 0   [(a3 + b3) = (a - b)(a2 + b2 - ab)]