If a + b + c = 14 , ab + bc + ca = 47 and abc = 15 then find the value of $$a^3 + b^3 + c^3$$.​

Correct option is D

Given:

a + b + c = 14 , ab + bc + ca = 47 and abc = 15

Formula Used:

​$$a^3 + b^3 + c^3 - 3abc = (a + b + c) \times \left[ (a + b + c)^2 - 3(ab + bc + ca) \right]$$

Solution:

​$$\begin{aligned}a^3 + b^3 + c^3 - 3abc &= 14 \times \left[ (14)^2 - 3 \times 47 \right] \\&\Rightarrow a^3 + b^3 + c^3 - 3 \times 15 = 14 \times (196 - 141) \\&\Rightarrow a^3 + b^3 + c^3 = 14 \times (55) + 45 \\&\Rightarrow 770 + 45 \\&\Rightarrow 815\end{aligned}$$

Hence, option (d) is the correct answer.