Trang chủ » Hỏi đáp » Môn Toán 7^2x + 7^2x+2 = 2450 x+2014/2 + 2x+4028 = x+2014/5 + x+2014/6 07/01/2025 7^2x + 7^2x+2 = 2450 x+2014/2 + 2x+4028 = x+2014/5 + x+2014/6
Giải đáp:$\begin{array}{l}a)x = 1\\b)x = – 2014\end{array}$ Lời giải và giải thích chi tiết: $\begin{array}{l}{7^{2x}} + {7^{2x + 2}} = 2450\\ \Leftrightarrow {7^{2x}} + {7^{2x}}{.7^2} = 2450\\ \Leftrightarrow {7^{2x}}.\left( {1 + 49} \right) = 2450\\ \Leftrightarrow {7^{2x}}.50 = 2450\\ \Leftrightarrow {7^{2x}} = 49\\ \Leftrightarrow {7^{2x}} = {7^2}\\ \Leftrightarrow 2x = 2\\ \Leftrightarrow x = 1\\Vậy\,x = 1\\\dfrac{{x + 2014}}{2} + 2x + 4028 = \dfrac{{x + 2014}}{5} + \dfrac{{x + 2014}}{6}\\ \Leftrightarrow \dfrac{{\left( {x + 2014} \right)}}{2} + 2.\left( {x + 2014} \right) – \dfrac{{\left( {x + 2014} \right)}}{5} – \dfrac{{\left( {x + 2014} \right)}}{6} = 0\\ \Leftrightarrow \left( {x + 2014} \right)\left( {\dfrac{1}{2} + 2 – \dfrac{1}{5} – \dfrac{1}{6}} \right) = 0\\ \Leftrightarrow \left( {x + 2014} \right) = 0\\ \Leftrightarrow x = – 2014\\Vậy\,x = – 2014\end{array}$ Trả lời
a)x = 1\\
b)x = – 2014
\end{array}$
{7^{2x}} + {7^{2x + 2}} = 2450\\
\Leftrightarrow {7^{2x}} + {7^{2x}}{.7^2} = 2450\\
\Leftrightarrow {7^{2x}}.\left( {1 + 49} \right) = 2450\\
\Leftrightarrow {7^{2x}}.50 = 2450\\
\Leftrightarrow {7^{2x}} = 49\\
\Leftrightarrow {7^{2x}} = {7^2}\\
\Leftrightarrow 2x = 2\\
\Leftrightarrow x = 1\\
Vậy\,x = 1\\
\dfrac{{x + 2014}}{2} + 2x + 4028 = \dfrac{{x + 2014}}{5} + \dfrac{{x + 2014}}{6}\\
\Leftrightarrow \dfrac{{\left( {x + 2014} \right)}}{2} + 2.\left( {x + 2014} \right) – \dfrac{{\left( {x + 2014} \right)}}{5} – \dfrac{{\left( {x + 2014} \right)}}{6} = 0\\
\Leftrightarrow \left( {x + 2014} \right)\left( {\dfrac{1}{2} + 2 – \dfrac{1}{5} – \dfrac{1}{6}} \right) = 0\\
\Leftrightarrow \left( {x + 2014} \right) = 0\\
\Leftrightarrow x = – 2014\\
Vậy\,x = – 2014
\end{array}$