Ta có:
\(a^2+8.5b^2+34\ge4ab+2b+8a\)
\(\Leftrightarrow\) \(2a^2+17b^2-8ab-4b-16a+68\ge0\)
\(\Leftrightarrow\left(a^2-8ab+16b^2\right)+\left(a^2-16a+64\right)+\left(b^2-4b+4\right)\ge0\)
\(\Leftrightarrow\left(a-4b\right)^2+\left(a-8\right)^2+\left(b-2\right)^2\ge0\) (Đúng)
Vậy \(a^2+8.5b^2+34\ge4ab+2b+8a\) (Đpcm)