$\frac{1}{a^2}+$ $\frac{1}{b^2}+$ $\frac{1}{c^2}=$ $\frac{b^2c^2+c^2a^2+a^2b^2}{(abc)^2}=$ $\frac{(ab+bc+ca)^2-2ab^2c-2abc^2-2a^2bc}{(abc)^2}=$ $(\frac{ab+bc+ca}{abc})^2-$ $\frac{2abc(a+b+c)}{(abc)^2}=$ $(\frac{1}{a}+$ $\frac{1}{b}+$ $\frac{1}{c})^2-$ $\frac{2(abc)^2}{(abc)^2}=2^2-2=4-2=2$