SSC CGL 2020 PYQ — Question 58

The correct answer is option 3 i.e 5/4

Explanation:

x⁴ + x²y² + y⁴ = 21

= x⁴ + x²y² + y⁴ + x²y² - x²y² = 21

= x⁴ + 2x²y² + y⁴ - x²y² = 21

(∵(a + b)² = a² + 2ab + b²)

= (x² + y²)² = 21 + x²y² -------(1)

x² + xy + y² = 7

x² + y² = 7 - xy -------(2)

From eq(1) and (2),

(7 - xy)² = 21 + x²y²

49 + x²y² - 14xy = 21 + x²y²

14xy = 49 - 21

xy = 28/14 = 2

From eq(2),

x² + y² = 7 - 2

x² + y² = 5

Now,

(1/x² + 1/y²)

(x² + y²)/(x² y²)

= 5/2²

= 5/4