Применим формулы возведения в квадрат разности и суммы:

\(\displaystyle \color{blue}{(\sqrt{6} - \sqrt{5})^{2}}+\color{green}{(\sqrt{6} + \sqrt{5})^{2}}=\)

\(\displaystyle \color{blue}{(\sqrt{6})^2 -2\cdot \sqrt{6}\cdot\sqrt{5}+(\sqrt{5})^{2}}+\color{green}{(\sqrt{6})^2 +2\cdot \sqrt{6}\cdot\sqrt{5}+(\sqrt{5})^{2}}{\small.}\)

Имеем:

• \(\displaystyle (\sqrt{6})^2=6{ \small ,}\)
• \(\displaystyle \color{blue}{ -2\cdot \sqrt{6}\cdot\sqrt{5}}+\color{green}{ 2\cdot \sqrt{6}\cdot\sqrt{5}=\color{red}{ 0}}{ \small ,}\)
• \(\displaystyle (\sqrt{5})^2=5{ \small .}\)

Значит,

\(\displaystyle \begin{aligned}\color{blue}{(\sqrt{6})^2 -\cancel{2\cdot \sqrt{6}\cdot\sqrt{5}}+(\sqrt{5})^{2}}+\color{green}{(\sqrt{6})^2 +\cancel{2\cdot \sqrt{6}\cdot\sqrt{5}}+(\sqrt{5})^{2}}=\\=6+5+6+5=22{\small.}\end{aligned}\)

Ответ: \(\displaystyle 22 {\small.} \)