If (a + b + c) = 6
a2 + b2 + c2 = 32
a3 + b3 + c3 = 189
find the value of abc + 3
Answer & explanation
Correct answer: option 4
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
36 = a2 + b2 + c2 + 2(ab + bc + ca)
36 = 32 + 2(ab + bc + ca)
ab + bc + ca = 2
Now → a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
189 – 3abc = 6(32 – 2)
abc = 3
abc + 3 = 6