Question

( frac{3-sqrt{5}}{3+2 sqrt{5}}=a sqrt{5}-frac{b}{11} )
( left(frac{3 sqrt{5}}{3+2 sqrt{5}}right)left(frac{3-2 sqrt{5}}{3-2 sqrt{5}}right)=9 sqrt{5}-frac{6}{11} )
( frac{9-6 sqrt{5}-3 sqrt{5}+2 times 5}{(3)^{2}-(2 sqrt{5})^{2}}=9 sqrt{5}-frac{b}{11} )
( frac{9-9 sqrt{5}+10}{9-4 times 5}=sqrt[4]{5}-frac{-b}{11} )
( Rightarrow quad frac{19-9 sqrt{5}}{9-20}=9 sqrt{5}-frac{5}{11} )
( Rightarrow quad frac{19-9 sqrt{5}}{-11}=9 sqrt{5}-frac{b}{11} )
( Rightarrow quad frac{-19}{11}+frac{3 sqrt{5}}{11}=9 sqrt{5}-frac{b}{11} )
( Rightarrow quad frac{9}{11} sqrt{5}-frac{19}{11}=9 sqrt{5}-frac{5}{11} )
Compaling both sldes,
( d=frac{9}{11} & cdot b=19 )

# 4. Find a and b in 3ts. 3te cass-6

Solution