Lời giải:
Ta có: \(2^x+2^y=2^{x+y}\)
\(\Leftrightarrow 2^x+2^y-2^x.2^y=0\)
\(\Leftrightarrow 2^x(1-2^y)-(1-2^y)=-1\)
\(\Leftrightarrow (2^x-1)(1-2^y)=-1\)
\(\Leftrightarrow (2^x-1)(2^y-1)=1\). Với \(x,y\in\mathbb{N}\Rightarrow 2^x-1, 2^y-1\geq 0\). Do đó:
\(\Rightarrow \left\{\begin{matrix} 2^x-1=1\\ 2^y-1=1\end{matrix}\right.\)\(\Leftrightarrow \left\{\begin{matrix} 2^x=2\\ 2^y=2\end{matrix}\right.\Leftrightarrow x=y=1\)
(Thỏa mãn)
Vậy \(x=y=1\)
Đúng 1
Bình luận (0)
