Question

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

A) 189 B) 243 C) 361 D) 486

Answer 1

Step-by-step explanation:

Given -

• a + b + c = 9
• ab + bc + ca = 18

→ -(-ab - bc - ca) = 18

→ -ab - bc - ca = -18

To Find -

• Value of a³ + b³ + c³ - 3abc is what ?

As we know that :-

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

Now,

• a + b + c = 9

Squaring both sides :-

→ (a + b + c)² = (9)²

→ a² + b² + c² + 2(ab + bc + ca) = 81

→ a² + b² + c² + 2(18) = 81

→ a² + b² + c² = 81 - 36

→ a² + b² + c² = 45

Now,

→ a³ + b³ + c³ - 3abc = (9)(45 - 18)

→ a³ + b³ + c³ - 3abc = 9 × 27

→ a³ + b³ + c³ - 3abc = 243

Hence,

Option 2 is correct.