SSC CGL 2020 PYQ — Question 67

The correct answer is option 2 i.e 1323

Explanation:

⇒ a + b + c = 9

⇒ ab + bc + ca = -22

We need to find the value of a³ + b³ + c³- 3abc

We know,

⇒ a³ + b³ + c³- 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

Now we need to find the value of a² + b² + c²

We also know,

⇒ (a + b + c)² = a² + b² + c² + 2( ab + bc + ca )

Putting the value of a + b + c = 9 and ab + bc + ca = -22

⇒ (9)² = a² + b² + c² + 2(-22)

⇒ 81 = a² + b² + c² -44

⇒ a² + b² + c² = 81 + 44

⇒ a² + b² + c² = 125

Now,

Substituting value in the formula for a³ + b³ + c³- 3abc

⇒ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

⇒ a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - (ab + bc + ca))

⇒ a³ + b³ + c³ - 3abc = (9)(125 + 22)

⇒ a³ + b³ + c³ - 3abc = (9)(147)

⇒ a³ + b³ + c³ - 3abc = 1323