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Bài nay nhiều cách giải . Bạn đặt k đi. MK đang bận để mai kt nên k kịp giải . Để tối mai mk giải cho
\(\left|x-3\right|=\left|2x+15\right|\)
\(\Rightarrow\orbr{\begin{cases}2x+15=x-3\\2x+15=3-x\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-18\\x=-4\end{cases}}}\)
KL:..................................................................
\(\left|2x-4\right|+\left|2x-6\right|=2\)
\(\Rightarrow\left|2x-4\right|+\left|6-2x\right|=2\)
Ta có: \(\hept{\begin{cases}\left|2x-4\right|\ge2x-4\forall x\\\left|6-2x\right|\ge6-2x\forall x\end{cases}\Rightarrow\left|2x-4\right|+\left|6-2x\right|\ge2x-4+6-2x=2\forall x}\)
Mà \(\left|2x-4\right|+\left|2x-6\right|=2\)
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}\left|2x-4\right|=2x-4\\\left|6-2x\right|=6-2x\end{cases}\Leftrightarrow\hept{\begin{cases}2x-4\ge0\\6-2x\ge0\end{cases}\Leftrightarrow}\hept{\begin{cases}x\ge2\\x\le3\end{cases}\Rightarrow}2\le x\le3}\)
KL:.............................................................
Câu c tương tự câu b
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)
\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)
\(\Rightarrow\frac{4^6}{3^6}.\frac{6^6}{2^6}=2^x\)
\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)
\(\Rightarrow\frac{\left(4.6\right)^6}{\left(3.2\right)^6}=2^x\)
\(\Rightarrow\frac{24^6}{6^6}=2^x\)
\(\Rightarrow4^6=2^x\)
\(\Rightarrow\left(2^2\right)^6=2^x\)
\(\Rightarrow2^{2.6}=2^x\)
\(\Rightarrow2^{12}=2^x\)
\(\Rightarrow x=12\)
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x.\)
\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)
\(\Rightarrow\frac{2^6.2^6.2^6.3^6}{3^6.2^6}=2^x\)\(\Rightarrow2^6.2^6=2^x\)
\(\Rightarrow2^{12}=2^x\Leftrightarrow x=12\)
\(=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}=\frac{3^3.2^3+3^3.3.2^2+3^3}{-13}=\frac{3^3\left(2^3+3.2^2+1\right)}{-13}=\frac{27.21}{-13}=\frac{-567}{13}\)
Ta có: \(\left|2x-\frac{5}{6}\right|=\left|x+\frac{1}{3}\right|\)
\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{5}{6}=x+\frac{1}{3}\\2x-\frac{5}{6}=-x-\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{6}\\3x=\frac{1}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=\frac{1}{6}\end{cases}}\)
\(|2x-\frac{5}{6}|=|x+\frac{1}{3}|\)
\(\orbr{\begin{cases}2x-\frac{5}{6}=x+\frac{1}{3}\\2x-\frac{5}{6}=-\left(x+\frac{1}{3}\right)\end{cases}}\)
\(\orbr{\begin{cases}2x-x=\frac{5}{6}+\frac{1}{3}\\2x-\frac{5}{6}=-x-\frac{1}{3}\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{7}{6}\\2x+x=-\frac{1}{3}+\frac{5}{6}\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{7}{6}\\3x=\frac{1}{2}\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{7}{6}\\x=\frac{1}{6}\end{cases}}\)
\(\frac{6^6+6^3.3^3+3^6}{-73}=\frac{3^6.\left(2^6+2^3+1\right)}{-73}=\frac{3^6.73}{\left(-73\right)}=-3^6=-729\)