If (3a + 1)² + (b - 1)² + (2c - 3)² = 0 then the value of (3a + b + 2c) is equal to?

Solution (By Examveda Team)

$$\eqalign{ & {\left( {3a + 1} \right)^2} + {\left( {b - 1} \right)^2} + {\left( {2c - 3} \right)^2} = 0 \cr & {\left( {3a + 1} \right)^2} = 0 \cr & \Rightarrow 3a = - 1 \cr & \Rightarrow a = - \frac{1}{3} \cr & {\left( {b - 1} \right)^2} = 0 \cr & \Rightarrow b - 1 = 0 \cr & \Rightarrow b = 1 \cr & {\left( {2c - 3} \right)^2} = 0 \cr & \Rightarrow c = \frac{3}{2} \cr & \therefore 3a + b + 2c \cr & = 3 \times - \frac{1}{3} + 1 + \frac{3}{2} \times 2 \cr & = - 1 + 1 + 3 \cr & = 3 \cr} $$