If a⁴ + 1 = $$\left[ {\frac{{{{\text{a}}^2}}}{{{{\text{b}}^2}}}} \right]$$ (4b² - b⁴ - 1), then what is the value of a⁴ + b⁴?

Solution (By Examveda Team)

$$\eqalign{ & {a^4} + 1 = \left( {\frac{{{a^2}}}{{{b^2}}}} \right)\left( {4{b^2} - {b^4} - 1} \right) \cr & {\text{take }}a = b = 1 \cr & 1 + 1 = \frac{1}{1}\left( {4 - 1 - 1} \right) \cr & 2 = 2{\text{ satisfied}} \cr & \therefore \,{a^4} + {b^4} = 1 + 1 = 2 \cr} $$