If ab = 21 and $$\frac{{{{\left( {a + b} \right)}^2}}}{{{{\left( {a - b} \right)}^2}}}$$   = $$\frac{{25}}{4}{\text{,}}$$  then the value of a² + b² + 3ab is?

Solution(By Examveda Team)

$$\eqalign{ & \frac{{{{\left( {a + b} \right)}^2}}}{{{{\left( {a - b} \right)}^2}}} = \frac{{25}}{4} \cr & \Rightarrow \frac{{a + b}}{{a - b}} = \frac{5}{2} \cr & \Rightarrow {\text{By Componendo & Dividendo}} \cr & \Rightarrow \frac{{a + b + a - b}}{{a + b - a + b}} = \frac{{5 + 2}}{{5 - 2}} \cr & \Rightarrow \frac{{2a}}{{2b}} = \frac{7}{3} \cr & \Rightarrow \frac{a}{b} = \frac{7}{3} \cr & {\text{Now, the value of}} \cr & \Rightarrow {a^2} + {b^2} + 3ab \cr & \Rightarrow {7^2} + {3^2} + 3.7.3 \cr & \Rightarrow 49 + 9 + 63 \cr & \Rightarrow 121 \cr} $$