SSC CGL 2022 PYQ — Question 53

The correct answer is option 4 i.e. 0

Given,

⇒ a + b + c = 6

⇒ a² + b² + c² = 32

⇒ a³ + b³ + c³ = 189

now, from (a + b + c)²   =   a² + b² + c²  + 2(ab + bc + ca)

⇒ 36 = 32 + 2(ab + bc + ca)

⇒ ab + bc + ca = 2

thus, from a³ + b³ + c³ - 3abc = (a + b + c)[(a² + b² + c² ) - (ab + bc + ca)]

⇒ 189 - 3abc = 6 × 32 - 2

⇒ 189 - 3abc = 6 × 30

⇒ 3abc = 189 - 180 = 9

⇒ abc = 3 

So, abc - 3 = 3 - 3 = 0