Question

If a + b + c = 9 and a²+b²+c²= 35, find the value of a³+b³ +c³-3abc.

Answer 1

(a + b + c) = 9

Squaring on both the sides, we get

(a + b + c)² = 9²

→ a² + b²+ c²  + 2(ab + bc + ca) = 81

→ 35  + 2(ab + bc + ca) = 81

→ 2(ab + bc + ca) = 81 – 35 = 46

→ ab + bc + ca = 23  ------>  (1)

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

                                      = 9(35 – 23)

                                      = 9(12) = 108

Hence, the answer is 108

Hope it helps!

Brainliest please! :)