Question

if a+b+c=3,a2+b2+c2=5 and a3+b3+c3=9 find the vakue of abc

Answer 1

here's the answer............

Answer 2

Given (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+c3-3abc = (a + b + c)( a2 + b2 + c2 – ab – bc – ca)
= 9(35 – 23)
= 9(12) = 108