Question

If a + b + c = 11 and ab + bc + ca = 20, then the value of the expression a³ + b³ + c³ - 3abc will be

(a) 121 

(b) 341 

(c) 671 

(d) 781

Answer 1

(c) 671

(a+ b + c)² = a² + b² + c² = 11² -2 x 20 = 121 - 40 = 81

Also, we know that

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

⇒ a³ + b³ + c³ - 3abc = 11 x (80-20)

⇒ a³ + b³ + c³ - 3abc = 11 x 61 = 671.