Toán Lớp 7: Giúp em với! Tìm $m$ và $n$ khi $2^m+2^n=2^{m+n}$.

Question

Toán Lớp 7:  Giúp em với! Tìm $m$ và $n$ khi $2^m+2^n=2^{m+n}$.

minhtamnguyet88 · Answer

$2^{m}$+$2^{n}$ =$2^{m+n}$    $2^{m}$ +$2^{n}$=$2^{n}$. $2^{m}$   $2^{m}$= $2^{m}$.$2^{n}$- $2^{n}$   $2^{m}$=$2^{n}$($2^{m}$-1)   $2^{m}$-1=$2^{n}$($2^{m}$-1)-1   $2^{n}$($2^{m}$-1)-($2^{m}$-1)=1   ($2^{m}$-1)($2^{n}$-1)=1   &rArr;$2^{m}$-1=1 v&agrave; $2^{n}$-1=1 ( trường hợp -1 kh&ocirc;ng thể xảy ra ở đ&acirc;y)   Giải    $2^{m}$-1=1       $2^{m}$=1+1       $2^{m}$=2                m=1   $2^{n}$-1=1      $2^{n}$=1+1     $2^{n}$=2               n=1   Vậy (m,n)=(1,1)

dongoclandiem · Answer

Giải đáp:   m=n=1    Lời giải và giải thích chi tiết:   2^{m}+2^{n}=2^{m+n}   &hArr; 2^{m}+2^{n}-2^{m+n}=0   &hArr; 2^{m+n}-2^{m}-2^{n}=0   &hArr; 2^{m}(2^{n}-1)-(2^{n}-1)=1   &hArr; (2^{n}-1)(2^{m}-1)=1   &hArr;  ( left[  begin{array}{l}2^n-1=1  2^m-1=1 end{array}  right. )    &hArr;  ( left[  begin{array}{l}2^n=2  2^m=2 end{array}  right. )    &hArr; m=n=1