[tex]m(3\sqrt2-2)+n(5\sqrt2-3)=7\sqrt2-5\\
3m\sqrt2-2m+5n\sqrt2-3n=7\sqrt2-5\\
\sqrt2(3m+5n)-2m-3n=7\sqrt2-5\\
Obtinem\ sistemul:\\
\left \{ {{3m+5n=7} \atop {-2m-3n=-5}} \right. \Leftrightarrow \left \{ {{6m+10n=14} \atop {-6m-9n=-15}} \right.\\
Le\ adunam: / n=-1\\
Inlocuim:
6m-10=14\\
6m=24\Rightarrow m=4[/tex]