\(A=\frac{2}{a^2+b^2}+\frac{35}{ab}+2ab\)
\(=\frac{2}{a^2+b^2}+\frac{2}{2ab}+\frac{32}{ab}+2ab+\frac{2}{ab}\)
\(\ge\frac{2\sqrt{2^2}}{\left(a+b\right)^2}+2\sqrt{\frac{32}{ab}\cdot2ab}+\frac{2}{\frac{\left(a+b\right)^2}{4}}\)
\(\ge\frac{1}{2}+2\cdot8+\frac{1}{2}=17\)