SSC CHSL 2021 PYQ — Question 53

The correct answer is option 4 i.e. 3026

x⁴ + y⁴ = (x² + y²)² - 2x²y²   ----(1)

x³ + y³ = (x + y) (x² + y² - xy)

$\frac{468}{12}$ = (x² + y² - xy)   

39 = (x² + y² - xy)    -----(2)

(x+y)² = x² + y² + 2xy

144 = x² + y² + 2xy

x² + y² = 144 - 2xy    ------(3)

Putting x² + y² in eqⁿ(2)

 39 = (144 - 2xy - xy)

We get xy = 35 & x² + y² = 74

Now,

x⁴ + y⁴ = (74)² - 2(35)²

⇒ 5476 - 2450

⇒ 3026