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SSC CGL 2019 PYQ — Question 63

SSC CGL - 4th June 2019 - Shift 3 • Quantitative Aptitude • Q63

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If x + y = 1 and xy(xy – 2) = 12, then the value of x4 + y4 is: 

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Correct answer: D

Explanation

Correct Answer is option 4 i.e. 25

Understanding

Application

Given:

x + y = 1 and xy(xy – 2) = 12

x + y = 1

Squaring:

(x + y)2 = 1

⇒ x2 + y2 + 2xy = 1

⇒ x2 + y2 = 1 – 2xy

Again, taking square: 

⇒ (x2 + y2)2 = (1 – 2xy)2

⇒ x4 + y4 + 2x2y2 = 1 + 4x2y2 – 4xy

⇒ x4 + y4 = 1 + 2x2y2 – 4xy

⇒ x4 + y4 = 1 + 2xy (xy – 2)

⇒ x4 + y4 = 1 + 2 × 12

⇒ x4 + y4 = 25