2m=2n+1024
\(\Leftrightarrow2^m-2^n=1024=2^{10}\)
\(\Leftrightarrow2^n\left(2^{m-n}-1\right)=2^{10}\)
Nếu \(m-n=0\) (vô lý)
Nếu \(m-n>0\)
\(\Rightarrow2^{m-n}-1\) lẻ mà 28 chẵn
\(\Rightarrow2^{m-n}-1=1\Rightarrow m=n+1\)
\(\Rightarrow2^n=2^8\Rightarrow n=8\Rightarrow m=n+1=8+1=9\)
Vậy n=8;m=9
2m=2n+1024
\(\Leftrightarrow2^m-2^n=1024=2^{10}\)
\(\Leftrightarrow2^n\left(2^{m-n}-1\right)=2^{10}\)
Nếu m-n=0 (vô lý)
Nếu m-n>0
\(\Rightarrow2^{m-n}-1\) lẻ mà 28 chẵn
\(\Rightarrow2^{m-n}-1=1\)\(\Rightarrow m=n+1\)
\(\Rightarrow2^n=2^{10}\Rightarrow n=10\Rightarrow m=n+1=10+1=11\)
Vậy n=10; m=11
Ta có:\(2^m=2^n+1024\)
\(\Leftrightarrow2^m-2^n=1024=2^{10}\)
\(\Leftrightarrow2^n\left(2^{m-n}-1\right)=2^{10}\)
Nếu m-n=0(vô lí) (loại)
Nếu m-n>0
\(\Rightarrow\)\(2^{m-n}-1\) lẻ mà 2\(^8\)chẵn
\(\Rightarrow2^{m-n}-1=1\Rightarrow m=n+1\)
\(\Rightarrow2^n=2^8\Rightarrow n=8\)
mà: m=n+1
\(\Rightarrow m=8+1=9\)
vậy m=9;n=8
chúc bạn càng ngày càng học giỏi nha
