If a² + b² + c² + 84 = 4(a - 2b + 4c), then $$\sqrt {ab - bc + ca} $$    is equal to:

Solution (By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} + {c^2} + 84 = 4\left( {a - 2b + 4c} \right) \cr & a = 2 \cr & b = - 4 \cr & c = 8 \cr & = \sqrt {ab - bc + ca} \cr & = \sqrt {2 \times \left( { - 4} \right) - \left( { - 4} \right) \times 8 + 8 \times 2} \cr & = \sqrt {32 + 8} \cr & = \sqrt {40} \cr & = 2\sqrt {10} \cr} $$