\(2^k\left(1+2^k\right)=20\)
\(2^k.2^k+2^k=20\)
\(2^k.2^k+\dfrac{2^k}{2}+\dfrac{2^k}{2}+\dfrac{1}{4}=\dfrac{84}{4}\)
\(2^k\left(2^k+\dfrac{1}{2}\right)+\dfrac{1}{2}\left(2^k+\dfrac{1}{2}\right)=\dfrac{81}{4}\)
\(\left(2^k+\dfrac{1}{2}\right)^2=\left(\dfrac{9}{2}\right)^2\) \(\Leftrightarrow\left[{}\begin{matrix}2^k+\dfrac{1}{2}=\dfrac{9}{2};2^k=\dfrac{9-1}{2}=4;k=2\\2^k+\dfrac{1}{2}=-\dfrac{9}{2};2^k=-\dfrac{5}{2}\left(voN_0\right)\end{matrix}\right.\)
kết luận
k =2
