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e) \(2^x+2^{x+3}=144\)
\(\Leftrightarrow2^x+2^x.2^3=144\)
\(\Leftrightarrow2^x.\left(1+8\right)=144\)
\(\Leftrightarrow2^x.9=144\)
\(\Rightarrow2^x=144:9=16\)
Ta có :\(2^4=16\Rightarrow x=4\)
l)\(0,2:1\frac{1}{5}=\frac{2}{3}:\left|6x+7\right|\)
\(\Leftrightarrow\frac{2}{3}:\left|6x+7\right|=\frac{1}{6}\)
\(\Rightarrow\left|6x+7\right|=\frac{2}{3}:\frac{1}{6}\)
\(\Rightarrow\left|6x+7\right|=4\)
\(\Rightarrow\orbr{\begin{cases}6x+7=4\\6x+7=-4\end{cases}\Rightarrow\orbr{\begin{cases}6x=-3\\6x=-11\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{1}{2}\\x=-\frac{11}{6}\end{cases}}}\)
\(\left|3x-1\right|\le7\)
\(\Rightarrow-7\le3x-1\le7\Rightarrow-6\le3x\le8\Rightarrow-2\le x\le\frac{8}{3}\)
\(\Delta=\left(-3\right)^2-4.\left(-1\right).4=9+16=25>0\)
\(\Delta>0\) thì pt có 2 nghiệm phân biệt \(\left\{{}\begin{matrix}x_1=\dfrac{3-5}{8}=-\dfrac{1}{4}\\x_2=\dfrac{3+5}{8}=1\end{matrix}\right.\)
\(Ta\) \(có\) \(4x^2-3x-1=0\)
\(\Rightarrow\) \(4x^2-4x+x-1=0\)
\(\Rightarrow\) \(4x.\left(x-1\right)+\left(x-1\right)=0\)
\(\Rightarrow\) \(\left(x-1\right).\left(4x+1\right)=0\)
\(\Rightarrow\) \(\left[{}\begin{matrix}x-1=0\\4x+1=0\end{matrix}\right.\) \(\Rightarrow\) \(\left[{}\begin{matrix}x=1\\x=\dfrac{-1}{4}\end{matrix}\right.\)
\(Vậy\) \(đa\) \(thức\) \(có\) \(nghiệm\) \(x=1\) \(hoặc\) \(x=\dfrac{-1}{4}\)
\(\left(\frac{5}{x+3}-2\right).4=7-\left(\frac{9}{x+3}+\frac{1}{2}\right).2\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\frac{18}{x+3}+1\)
\(\Leftrightarrow\frac{20}{x+3}-8=8-\frac{18}{x+3}\)
\(\Leftrightarrow\frac{20}{x+3}+\frac{18}{x+3}=8+8\)
\(\Leftrightarrow\frac{38}{x+3}=16\)
\(\Leftrightarrow x+3=2,375\)
\(\Leftrightarrow x=-0,625\)
\(\left(\frac{5}{x+3}-2\right).4=7-\left(\frac{9}{x+3}+\frac{1}{2}\right).2\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\left(\frac{18}{x+3}+1\right)\)
\(\Leftrightarrow\frac{20}{x+3}-8=7-\frac{18}{x+3}-1\)
\(\Leftrightarrow\frac{20}{x+3}+\frac{18}{x+3}=7-1+8\)
\(\Leftrightarrow\frac{38}{x+3}=14\)
\(\Leftrightarrow\left(x+3\right)14=38\)
\(\Leftrightarrow14x+42=38\)
\(\Leftrightarrow14x=-4\Leftrightarrow x=-\frac{4}{14}=-\frac{2}{7}\)
Vậy \(x=-\frac{2}{7}\)
﴾ 1‐1/2﴿ . ﴾1‐1/3﴿.﴾1‐1/4﴿.......﴾1‐1/2016﴿ . ﴾1‐1/2017﴿
=1/2.2/3.3.4x...x2015/2016.2016/2017
=1.2.3.4. ... .2015.2016/2.3.4.5. ... .2016.2017
=1/2017
mk viết thiếu : cái cuối cùng là :[1+1/n] nhã
1 + 1+ 2 = 4 nha Bùi Hoàng Linh Chi
1+1+2= 4 nha