Question

If a + b + c = 6, a³ + b³ + c³ - 3 abc = 342, and a² + b² + c² = 50, then what is the value of ab + bc + ca?

• A. 5
• B. -5
• C. -7
• D. 8

Answer 1

Answer:

C. -7

Solution:

Given :-

If a + b + c = 6, a³ + b³ + c³ - 3abc = 342, and a² + b² + c2 = 50

Concept :- 

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

Calculation :-

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

⇒ 342 = 6 $\times$ (50 - ab - bc - ca)

⇒ $(\frac{342}{6})$ = 50 - (ab + bc + ca)

⇒ 57 = 50 - (ab + bc + ca)

⇒ (ab + bc + ca) = 50 - 57 

⇒ (ab + bc + ca) = -7

∴ (ab + bc + ca) is -7