Evaluate the expression
\[ \frac{5x^2+10x+10}{(x+1)^4-1}\]
for \( x=\sqrt5-2 \) and write the result in the form \( a+b\sqrt c \), where \( a \), \( b \), \( c \) are natural numbers.
Let
\[ a=\left[\left(2-\sqrt3\right)^{\frac12}+\left(2+\sqrt3\right)^{\frac12}\right]^2,\ b=\frac{81^{-1}\cdot\sqrt3}{27^{-2}\cdot\sqrt[4]9}.\]
Comparing the numbers \( a^b \) and \( b^a \) you get:
The bank offers a term deposit with annual interest rate of \( 0.9\% \). We need to tax our profits with the income tax of \( 15\% \). How many Euros are we going to have after five years of savings if the original deposit is \( 200 \) Euros?