If a + b + c = 11 and ab + bc + ca = 20, then the value of the express

1.	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» (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.

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»

(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.