\[ (3 x-2)^{2}-(x+3)^{2}=0 \] 11. What is the absolute value of the difference between the two roots of the above equation?

7. Show that the set F of the six complex valued functions: \( f_{1}(z)=z, f_{2}(z)=\frac{1}{1-z}, f_{3}(z)=\frac{z-1}{z} \) \( f_{4}(z)=\frac{1}{z}, f_{5}(z)=1-z, f_{6}(z)=\frac{z}{z-1} \) is a group under the usual multiplication of mappings.

Solve for \( x \) and \( y \) simultaneously: \( 3^{x+y}=27 \quad \) and \( \quad x^{2}+y^{2}=17 \)

The ratio between the sum of the fifth, sixth and seventh terms of a geometric series and the sum of the first three terms of the same series is \( 81: 16 \). Determine the sum of the first ten terms, if the first term is 1024 .

5. In un rettangolo un lato misura 1 unità più dell'altro. Detta \( x \) la misura del lato minore, esprimi, in funzione di \( \left[A(x)=x^{2}+x+\frac{1}{4}\right] \)

\( 6 x^{3}-5 x^{7}+6 \) leading term? Leading cafficient? Turning Caint?