[tex]a=3-\sqrt5\\b=6+4\sqrt5\\\\a*b=(3-\sqrt5)(6+4\sqrt5)=18+12\sqrt5-6\sqrt5-20=-2+6\sqrt5\\\\\frac1{a}=\frac{1}{3-\sqrt5}*\frac{3+\sqrt5}{3+\sqrt5}=\frac{3+\sqrt5}{3^2-(\sqrt5)^2}=\frac{3+\sqrt5}{9-5}=\frac{3+\sqrt5}4\\\\b^2=(6+4\sqrt5)^2=6^2+2*6*4\sqrt5+(4\sqrt5)^2=36+48\sqrt5+80=116+48\sqrt5[/tex]
