SSC CGL 2021 PYQ — Question 66

The correct answer is option 1 i.e.  4 $\frac{2}{3}$

Given :

 x + y = 2 and $\frac{1}{x}$+$\frac{1}{y}$ = $\frac{18}{5}$ 

Formula used :

(a + b)³ = a³ + b³ + 3ab(a + b)        ----- (1)

Calculations :

⇒   $\frac{1}{x}$+$\frac{1}{y}$ = $\frac{18}{5}$ 

⇒ (x + y)/xy = 18/5

⇒ xy = 5/9

Using equation (1), we get

⇒ (x + y)³ = x³ + y³ + 3xy(x + y)

⇒ 2³ = x³ + y³ + 3(5/9)(2)

⇒ 8 = x³ + y³ + 10/3

⇒ x³ + y³ = 8 - 10/3

⇒ 14/3 = $4\frac{2}{3}$