Matematică
LudovicIulian
2015-11-09 10:52:39
Determinati m,n∈Q in urmatoarele conditii: a)(m-2)√2=n+√2 b)m(1+√2)²=3+n+2√2
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Radu32
2015-11-09 11:48:37

[latex]a)\ \ (m-2)sqrt2=n+sqrt2 Rightarrow 0+(m-2)sqrt2 = n+sqrt2 \ \ left{ egin{array}{c} 0 = n\ m-2 = 1 end{array} ight Rightarrow left{ egin{array}{c} n=0\ m = 3 end{array} ight | \ \ \ b)\ \ m(1+sqrt2)^2=3+n+2sqrt2 Rightarrow mcdot(1+2sqrt2+2) = 3+n+2sqrt2 Rightarrow \ \ Rightarrow mcdot (3+2sqrt2)=3+n+2sqrt2 Rightarrow 3m+mcdot2sqrt2 = 3+n+2sqrt2[/latex] [latex]left{ egin{array}{c} 3m = 3+n \ m = 1 end{array} ight Rightarrow left{ egin{array}{c} 3 = 3+n \ m = 1 end{array} ight Rightarrow left{ egin{array}{c} n=0 \ m = 1 end{array} ight |[/latex]

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