SSC Selection Post 2020 PYQ — Question 55

The correct answer is Option 1 i.e. 154.

a² + b² = $\frac{31}{9}$ 

[(a² + b²) = (a + b)² - 2ab]

⇒ $\frac{31}{9}$ = ($7\over3$)² - 2ab

⇒ 2ab = ${49\over9}-{31\over9}$ = $18\over9$ = 2

⇒ ab = 1

⇒​​​​​​​ (a³ + b³) = (a + b)³ - 3ab(a + b)

⇒​​​​​​​ (a³ + b³) = ($7\over3$)³ - 3 × 1 × $7\over3$

⇒​​​​​​​ (a³ + b³) = $343\over27$ - 7

⇒​​​​​​​ (a³ + b³) = $343-189\over27$ = $154\over27$

⇒​​​​​​​ 27(a³ + b³) = 154