If $${x^2} + \frac{1}{5}x + {a^2}$$   is a perfect square, then a is?

Solution (By Examveda Team)

$$\eqalign{ & {x^2} + \frac{1}{5}x + {a^2} \cr & {{\text{A}}^2} + {\text{2}} \times {\text{AB}} + {{\text{B}}^2} = {\left( {{\text{A}} + {\text{B}}} \right)^2} \cr & {x^2} + 2 \times \frac{1}{{10}} \times x + {a^2} = {\left( {x + \frac{1}{{10}}} \right)^2} \cr & {\text{A}} = x \cr & {\text{B}} = \frac{1}{{10}} \cr & {\text{B}} = a = \frac{1}{{10}} \cr} $$