Question

Determinati numerele rationale m si n pentru care : m(3√2 -2)+n(5√2-3)=7√2-5

Answer 1

[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]