SSC CPO 2019 PYQ — Question 102

The correct answer is Option 2 i.e. (5/8)

x⁴ + x²y² + y⁴ = x⁴ + 2x²y² + y⁴ - x²y²

= (x² + y²)² - (xy)²

= (x² + xy + y²) (x² - xy + y²)

⇒ (3/16) (x² - xy + y²) = 21/256

⇒ (x² - xy + y²) = (21 × 16)/(256 × 3) = 7/16

⇒ (x² - xy + y²) = 7/16

Given: x² + xy + y² = (3/16)

Adding both:

⇒ 2(x² + y²) = 10/16 = 5/8