[tex]a( \sqrt{2} + \sqrt{3} ) + b( \sqrt{2} - \sqrt{3} ) = \sqrt{18} + \sqrt{2} [/tex]
[tex] \sqrt{2}a + \sqrt{3} a + \sqrt{2} b - \sqrt{3} b = 3 \sqrt{2} + \sqrt{2} [/tex]
[tex] \sqrt{2} (a + b) + \sqrt{3}(a-b)= 4 \sqrt{2} [/tex]
[tex]\left\{\begin{matrix}
a + b = 4\\
a - b = 0\end{matrix}\right.[/tex]
[tex]a + a + b - b = 4 + 0[/tex]
[tex]2a = 4 \: | \div 2[/tex]
[tex]a = 2 \: \in \: \mathbb{Q}[/tex]
[tex]a + b = 4[/tex]
[tex]2 + b = 4[/tex]
[tex]b = 4 - 2[/tex]
[tex]b = 2 \: \in \: \mathbb{Q}[/tex]
[tex]S=\left\{(a,b)\right\}=\left\{(2,2)\right\}[/tex]
