2^a+2^b +2^c=112 (2^b-1)x2n=2394 (2^c-2)x2n=1140 2^c x2n=609 Tìm 2n, a, b, c Giải chi tiết hộ mình ạ 30/08/2021 Bởi Peyton 2^a+2^b +2^c=112 (2^b-1)x2n=2394 (2^c-2)x2n=1140 2^c x2n=609 Tìm 2n, a, b, c Giải chi tiết hộ mình ạ
Đáp án: $\begin{array}{l}\left\{ \begin{array}{l}{2^a} + {2^b} + {2^c} = 112\\\left( {{2^b} – 1} \right).2n = 2394\\\left( {{2^c} – 2} \right).2n = 1140\\{2^c}.2n = 609\end{array} \right. \Rightarrow \left\{ \begin{array}{l}{2^a} + {2^b} + {2^c} = 112\\\left( {{2^b} – 1} \right).2n = 2394\\{2^c}.2n – 4n = 1140\\{2^c}.2n = 609\end{array} \right. \Rightarrow \left\{ \begin{array}{l}{2^a} + {2^b} + {2^c} = 112\\\left( {{2^b} – 1} \right).2n = 2394\\{2^c}.2n = 609\\ – 4n = 1140 – 609\end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l}{2^a} + {2^b} + {2^c} = 112\\\left( {{2^b} – 1} \right).2n = 2394\\{2^c}.2n = 609\\ – 4n = 1140 – 609\end{array} \right.\left\{ \begin{array}{l}{2^a} + {2^b} + {2^c} = 112\\\left( {{2^b} – 1} \right).2n = 2394\\{2^c} = \frac{{ – 406}}{{177}}\left( {vo\,li} \right)\\n = – \frac{{531}}{4}\end{array} \right.\\ \Rightarrow pt\,vô\,nghiệm\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} – 1} \right).2n = 2394\\
\left( {{2^c} – 2} \right).2n = 1140\\
{2^c}.2n = 609
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} – 1} \right).2n = 2394\\
{2^c}.2n – 4n = 1140\\
{2^c}.2n = 609
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} – 1} \right).2n = 2394\\
{2^c}.2n = 609\\
– 4n = 1140 – 609
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} – 1} \right).2n = 2394\\
{2^c}.2n = 609\\
– 4n = 1140 – 609
\end{array} \right.\left\{ \begin{array}{l}
{2^a} + {2^b} + {2^c} = 112\\
\left( {{2^b} – 1} \right).2n = 2394\\
{2^c} = \frac{{ – 406}}{{177}}\left( {vo\,li} \right)\\
n = – \frac{{531}}{4}
\end{array} \right.\\
\Rightarrow pt\,vô\,nghiệm
\end{array}$