If a + b + c = 2, $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$$   = 0, ac = $$\frac{4}{b}$$ and a³ + b³ + c³ = 28, find the value of a² + b² + c².

A. 6

B. 12

C. 10

D. 8

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & a + b + c = 2 \cr & ab + bc + ca = 0 \cr & abc = 4 \cr & {a^3} + {b^3} + {c^3} - 3abc = \left( {a + b + c} \right)\left[ {\left( {{a^2} + {b^2} + {c^2}} \right) - \left( {ab + bc + ca} \right)} \right] \cr & 28 - 3 \times 4 = 2\left( {{a^2} + {b^2} + {c^2}} \right) \cr & {a^2} + {b^2} + {c^2} = 8 \cr} $$