Ta có:

$\left\{ \begin{align}& {{\left( \frac{1}{13}x-7 \right)}^{8}}\ge 0 \\  & {{\left( \frac{1}{17}y-7 \right)}^{6}}\ge 0 \\ \end{align} \right.$ với mọi x, y. Do đó: ${{\left( \frac{1}{13}x-7 \right)}^{8}}+{{\left( \frac{1}{17}y-7 \right)}^{6}}=0$ khi và chỉ khi

$\left\{ \begin{align}& {{\left( \frac{1}{13}x-7 \right)}^{8}}=0\Rightarrow x=91 \\  & {{\left( \frac{1}{17}y-7 \right)}^{6}}\ge 0\Rightarrow y=119 \\ \end{align}\right.$

Vậy  x + y = 91 + 119 = 210