Correct Answer - Option 3 : 3abc
Given,
a2 + b2 + c2 = 18% of 211(1/9)
a2 + b2 + c2 = 18 × (1900/900) = 38
Also given,
ab + bc + ca = –(a2 + b2 + c2)/2
ab + bc + ca = –38/2 = –19
We know that:
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b + c)2 = 38 + 2(–19)
(a + b + c)2 = 0
a + b + c = 0
We also know that:
a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
a3 + b3 + c3 – 3abc = 0
a
3 + b
3 + c
3 = 3abc