Question

Determinati m,n∈Q in urmatoarele conditii:
a)(m-2)√2=n+√2
b)m(1+√2)²=3+n+2√2

Answer 1

[tex]a)\\ \\ (m-2)\sqrt2=n+\sqrt2 \Rightarrow 0+(m-2)\sqrt2 = n+\sqrt2 \\ \\ \left\{ \begin{array}{c} 0 = n\\ m-2 = 1 \end{array} \right \Rightarrow \left\{ \begin{array}{c} n=0\\ m = 3 \end{array} \right | \\ \\ \\ b)\\ \\ m(1+\sqrt2)^2=3+n+2\sqrt2 \Rightarrow m\cdot(1+2\sqrt2+2) = 3+n+2\sqrt2 \Rightarrow \\ \\ \Rightarrow m\cdot (3+2\sqrt2)=3+n+2\sqrt2 \Rightarrow 3m+m\cdot2\sqrt2 = 3+n+2\sqrt2[/tex]

$\left\{ \begin{array}{c} 3m = 3+n \\ m = 1 \end{array} \right \Rightarrow \left\{ \begin{array}{c} 3 = 3+n \\ m = 1 \end{array} \right \Rightarrow \left\{ \begin{array}{c} n=0 \\ m = 1 \end{array} \right |$