Question

Tìm x,y thuộc N* biết : 2^x+2^y=72 ( x>y)

Answer 1

\(\Rightarrow2^y\left(2^{x-y}+1\right)=72\)

Vì \(2^{x-y}+1\) lẻ nên \(2^y\left(2^{x-y}+1\right)=72=2^3\cdot9\)

\(\Rightarrow\left\{{}\begin{matrix}y=3\\2^{x-3}+1=9\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=3\\2^{x-3}=8=2^3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=6\\y=3\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(6;3\right)\)