\(\frac{7^{x+2}+7^{x+1}+7x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
\(\Rightarrow\frac{7x\left(7^2+7^1+1\right)}{57}=\frac{5^{2x}\left(1+5^1+5^3\right)}{131}\)
\(\Rightarrow\frac{7x\left(49+7+1\right)}{57}=\frac{5^{2x}\left(1+5+125\right)}{131}\)
\(\Rightarrow\frac{7x.57}{57}=\frac{5^{2x}.131}{131}\)
\(\Rightarrow7x=25x\)
\(\Rightarrow x=0\)
\(\left(4x-3\right)^4=\left(4x-3\right)^2\)
\(\Rightarrow\left(4x-3\right)^4-\left(4x-3\right)^2=0\)
\(\Rightarrow\left(4x-3\right)^2\left[\left(4x-3\right)^2-1\right]=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(4x-3\right)^2=0\\\left(4x-3\right)^2=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}4x-3=0\\4x-3=-1\\4x-3=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{4}\\x=\frac{1}{2}\\x=1\end{cases}}\)
Bài mình làm sai à hay sao mà t]ick sai thế???
Bài làm:
a) \(\frac{7^{x+2}+7^{x+1}+7^x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
\(\Leftrightarrow\frac{7^x\left(7^2+7+1\right)}{57}=\frac{5^{2x}\left(1+5+5^3\right)}{131}\)
\(\Leftrightarrow\frac{7^x.57}{57}=\frac{25^x.131}{131}\)
\(\Rightarrow7^x=25^x\Rightarrow x=0\)
b) \(\left(4x-3\right)^4=\left(4x-3\right)^2\)
\(\Leftrightarrow\left(4x-3\right)^4-\left(4x-3\right)^2=0\)
\(\Leftrightarrow\left(4x-3\right)^2\left[\left(4x-3\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(4x-3\right)^2=0\\\left(4x-3\right)^2-1=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{3}{4}\\\left(4x-3\right)^2=1\end{cases}}\)
Nếu \(\left(4x-3\right)^2=1\Leftrightarrow\orbr{\begin{cases}4x-3=1\\4x-3=-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=1\\x=\frac{1}{2}\end{cases}}\)
Vậy \(x=\frac{3}{4}\)hoặc \(x=\frac{1}{2}\)hoặc \(x=1\)
Học tốt!!!!
