Найдите значение выражения (a^(1/2)-a^(1/4))*(a^(1/4)+1)*(a^(1/4)+a^(-1/4)), если a=41.

\[\left( a^{\frac{1}{2}} - a^{\frac{1}{4}} \right)\left( a^{\frac{1}{4}} + 1 \right)\left( a^{\frac{1}{4}} + a^{- \frac{1}{4}} \right) =\]

\[= \left( a^{\frac{1}{4}} - 1 \right)\left( a^{\frac{1}{4}} + 1 \right)\left( a^{\frac{1}{2}} + 1 \right) =\]

\[= \left( \left( a^{\frac{1}{4}} \right)^{2} - 1 \right)\left( a^{\frac{1}{2}} + 1 \right) =\]

\[= \left( a^{\frac{1}{2}}–1 \right)\left( a^{\frac{1}{2}} + 1 \right) =\]

\[= \left( a^{\frac{1}{2}} \right)^{2} - 1 = a - 1\]

\[a = 41:\]

\[a - 1 = 41 - 1 = 40.\]