The value of $$\frac{{{{\left( {4.6} \right)}^4} + {{\left( {5.4} \right)}^4} + {{\left( {24.84} \right)}^2}}}{{{{\left( {4.6} \right)}^2} + {{\left( {5.4} \right)}^2} + 24.84}}$$     is:

Solution (By Examveda Team)

$$\eqalign{ & 4.6 = b \cr & 5.4 = a \cr & \frac{{{b^4} + {a^4} + {a^2}{b^2}}}{{{a^2} + {b^2} + ab}} \cr & = \frac{{\left( {{a^2} + {b^2} + ab} \right)\left( {{a^2} + {b^2} - ab} \right)}}{{{a^2} + {b^2} + ab}} \cr & = {a^2} + {b^2} - ab \cr & = {\left( {a - b} \right)^2} + ab \cr & = {\left( {5.4 - 4.6} \right)^2} + 24.84 \cr & = {0.8^2} + 24.84 \cr & = 25.48 \cr} $$