a) Let $a+b+c=s$ then $ab+bc+ca=\frac{s^2-s}{2},abc=\frac{(a^3+b^3+c^3-(a+b+c)(a^2+b^2+c^2-ab-bc-ca))}{3}=\frac{s-s(s-\frac{s^2-s}{2})}{3}=\frac{s^3-3s^2+2s}{6}$ $\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{b}\right)(a+b+c-2)= \frac{\frac{s^2-s}{2}}{\frac{s^3-3s^2+2s}{6}}(s-2)=3$ b)$a=\frac{1}{2},b=\frac{1+\sqrt{\frac{3}{2}}}{2},c=\frac{1-\sqrt{\frac{3}{2}}}{2}$