Question

f (a + b + c) = 12, and (a² + b² + c²) = 50, find the value of (a³ + b³ + c³ - 3abc)

• A. 36
• B. 24
• C. 42
• D. 48

Answer 1

Answer:

A. 36

Solution:

Given : 

(a + b + c) = 12, (a² + b² + c²) = 50

Formula Used : 

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

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

Calculation : 

⇒ 144 = 50 + 2(ab + bc +ac)

⇒ (ab + bc +ac) = $\frac{94}{2} = 47$

Now,

⇒ (a³ + b³ + c³ - 3abc)

⇒ (a² + b² + c² - ab - bc - ca)(a + b + c) = (50 - 47)(12)

⇒ $3\times{12} = 36$

∴ The correct answer is 36.