Correct Answer - Option 3 : 2
Given :
a + b + c = 4 and a2 + b2 + c2 = 6
Formula used :
a3 + b3 + c3 – 3abc = (a + b + c)[(a + b + c)2 – 3(ab + bc + ca)]
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Calculations :
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
42 = 6 + 2(ab + bc + ca)
ab + bc + ca = 5
a3 + b3 + c3 – 3abc = 4[(4)2 – 3(5)]
⇒ 4(16 – 15)
⇒ 4
√(a3 + b3 + c3 – 3abc) = √4
⇒ 2
∴ The correct choice will be option 3
