Question

Q.18) If a + b + c = 11 and ab + bc + ca = 20 then find the value of: a3 + b3 + c3 - 3abc​

Answer 1

Answer

671

Explanation

(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.