Câu hỏi của Trần Minh Thắng

Question

$\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$$\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$\(\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}...

Xyz OLM · Accepted Answer

1) Ta có : $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$$\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$Vì $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0$=> x + 1 = 0=> x = - 1b) $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$=> $\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)=\left(\frac{x+2}{2008}+1\right)+\left(\frac{x+1}{2009}+1\right)$=> $\frac{x+2010}{2006}+\frac{x+2010}{2007}=\frac{x+2010}{2008}+\frac{x+2010}{2009}$=> $\left(x+2010\right)\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$Vì $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\ne0$=> x + 2010 = 0=> x = -2010c) $\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}{75}+\frac{x+1969}{69}$$\Rightarrow\left(\frac{x+1945}{45}-1\right)+\left(\frac{x+1954}{54}-1\right)=\left(\frac{x+1975}{75}-1\right)+\left(\frac{x+1969}{69}-1\right)$=> $\frac{x+1900}{45}+\frac{x+1900}{54}=\frac{x+1900}{75}+\frac{x+1900}{69}$=> $\left(x+1900\right)\left(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\right)=0$=> $x+1900=0\left(\text{Vì }\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\ne0\right)$=> x = -1900d) $\frac{x+2008}{10}+\frac{x+2010}{9}=\frac{x+2012}{8}+\frac{x+2014}{7}$=> $\left(\frac{x+2008}{10}+2\right)+\left(\frac{x+2010}{9}+2\right)=\left(\frac{x+2012}{8}+2\right)+\left(\frac{x+2014}{7}+2\right)$=> $\frac{x+2028}{10}+\frac{x+2028}{9}=\frac{x+2028}{8}+\frac{x+2028}{7}$=> $\left(x+2028\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\right)=0$=> x + 2028 = 0 $\left(\text{Vì }\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\ne0\right)$=> x = -2028Câu trả lời: 1) Ta có : $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$$\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$Vì $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0$=> x + 1 = 0=> x = - 1b) $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$=> $\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)=\left(\frac{x+2}{2008}+1\right)+\left(\frac{x+1}{2009}+1\right)$=> $\frac{x+2010}{2006}+\frac{x+2010}{2007}=\frac{x+2010}{2008}+\frac{x+2010}{2009}$=> $\left(x+2010\right)\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$Vì $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\ne0$=> x + 2010 = 0=> x = -2010c) $\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}{75}+\frac{x+1969}{69}$$\Rightarrow\left(\frac{x+1945}{45}-1\right)+\left(\frac{x+1954}{54}-1\right)=\left(\frac{x+1975}{75}-1\right)+\left(\frac{x+1969}{69}-1\right)$=> $\frac{x+1900}{45}+\frac{x+1900}{54}=\frac{x+1900}{75}+\frac{x+1900}{69}$=> $\left(x+1900\right)\left(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\right)=0$=> $x+1900=0\left(\text{Vì }\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\ne0\right)$=> x = -1900d) $\frac{x+2008}{10}+\frac{x+2010}{9}=\frac{x+2012}{8}+\frac{x+2014}{7}$=> $\left(\frac{x+2008}{10}+2\right)+\left(\frac{x+2010}{9}+2\right)=\left(\frac{x+2012}{8}+2\right)+\left(\frac{x+2014}{7}+2\right)$=> $\frac{x+2028}{10}+\frac{x+2028}{9}=\frac{x+2028}{8}+\frac{x+2028}{7}$=> $\left(x+2028\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\right)=0$=> x + 2028 = 0 $\left(\text{Vì }\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\ne0\right)$=> x = -2028

Tạ Đức Hoàng Anh · Answer

1) Ta có: $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$ $\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0$ $\Leftrightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$ + TH1: $x+1=0$$\Leftrightarrow$$x=-1$ + TH2: $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}=0$ Vì $\hept{\begin{cases}\frac{1}{10}>\frac{1}{13}\\frac{1}{11}>\frac{1}{14}\\frac{1}{12}>0\end{cases}}$$\Rightarrow$$\frac{1}{10}+\frac{1}{11}+\frac{1}{12}>\frac{1}{13}+\frac{1}{14}$ $\Rightarrow$$\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}>0$ mà $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-1$2) Ta có: $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$ $\Leftrightarrow\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)-\left(\frac{x+2}{2008}+1\right)-\left(\frac{x+1}{2009}+1\right)=0$ $\Leftrightarrow\frac{x+2010}{2006}+\frac{x+2010}{2007}-\frac{x+2010}{2008}-\frac{x+2010}{2009}=0$ $\Leftrightarrow\left(x+2010\right).\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$ + TH1: $x+2010=0$$\Leftrightarrow$$x=-2010$ + TH2: $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}=0$ Vì $\hept{\begin{cases}\frac{1}{2006}>\frac{1}{2008}\\frac{1}{2007}>\frac{1}{2009}\end{cases}}$$\Rightarrow$$\frac{1}{2006}+\frac{1}{2007}>\frac{1}{2008}+\frac{1}{2009}$ $\Rightarrow$$\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}>0$ mà $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-2010$3) Ta có: $\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}{75}+\frac{x+1969}{69}$ $\Leftrightarrow\left(\frac{x+1945}{45}-1\right)+\left(\frac{x+1954}{54}-1\right)-\left(\frac{x+1975}{75}-1\right)-\left(\frac{x+1969}{69}-1\right)=0$ $\Leftrightarrow\frac{x+1900}{45}+\frac{x+1900}{54}-\frac{x+1900}{75}-\frac{x+1900}{69}=0$ $\Leftrightarrow\left(x+1900\right).\left(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\right)=0$ + TH1: $x+1900=0$$\Leftrightarrow$$x=-1900$ + TH2: $\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}=0$ Vì $\hept{\begin{cases}\frac{1}{45}>\frac{1}{75}\\frac{1}{54}>\frac{1}{69}\end{cases}}$$\Rightarrow$$\frac{1}{45}+\frac{1}{54}>\frac{1}{75}+\frac{1}{69}$ $\Rightarrow$$\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}>0$ mà $\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-1900$4) Ta có: $\frac{x-99}{5}+\frac{x-97}{7}=\frac{x-95}{9}+\frac{x-93}{11}$ $\Leftrightarrow\left(\frac{x-99}{5}-1\right)+\left(\frac{x-97}{7}-1\right)-\left(\frac{x-95}{9}-1\right)-\left(\frac{x-93}{11}-1\right)=0$ $\Leftrightarrow\frac{x-104}{5}+\frac{x-104}{7}-\frac{x-104}{9}-\frac{x-104}{11}=0$ $\Leftrightarrow\left(x-104\right).\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)=0$ + TH1: $x-104=0$$\Leftrightarrow$$x=104$ + TH2: $\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}=0$ Vì $\hept{\begin{cases}\frac{1}{5}>\frac{1}{7}\\frac{1}{9}>\frac{1}{11}\end{cases}}$$\Rightarrow$$\frac{1}{5}+\frac{1}{7}>\frac{1}{9}+\frac{1}{11}$ $\Rightarrow$$\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}>0$ mà $\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=104$5) Ta có: $\frac{x+2008}{10}+\frac{x+2010}{9}=\frac{x+2012}{8}+\frac{x+2014}{7}$ $\Leftrightarrow\left(\frac{x+2008}{10}+2\right)+\left(\frac{x+2010}{9}+2\right)-\left(\frac{x+2012}{8}+2\right)-\left(\frac{x+2014}{7}+2\right)=0$ $\Leftrightarrow\frac{x+2028}{10}+\frac{x+2028}{9}-\frac{x+2028}{8}-\frac{x+2028}{7}=0$ $\Leftrightarrow\left(x+2028\right).\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\right)=0$ + TH1: $x+2028=0$$\Leftrightarrow$$x=-2028$ + TH2: $\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}=0$ Vì $\hept{\begin{cases}\frac{1}{10}< \frac{1}{8}\\frac{1}{9}< \frac{1}{7}\end{cases}}$$\Rightarrow$$\frac{1}{10}+\frac{1}{9}< \frac{1}{8}+\frac{1}{7}$ $\Rightarrow$$\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}< 0$ mà $\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-2028$Chúc bn hok tốt nhaCâu trả lời: 1) Ta có: $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$ $\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0$ $\Leftrightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$ + TH1: $x+1=0$$\Leftrightarrow$$x=-1$ + TH2: $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}=0$ Vì $\hept{\begin{cases}\frac{1}{10}>\frac{1}{13}\\frac{1}{11}>\frac{1}{14}\\frac{1}{12}>0\end{cases}}$$\Rightarrow$$\frac{1}{10}+\frac{1}{11}+\frac{1}{12}>\frac{1}{13}+\frac{1}{14}$ $\Rightarrow$$\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}>0$ mà $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-1$2) Ta có: $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$ $\Leftrightarrow\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)-\left(\frac{x+2}{2008}+1\right)-\left(\frac{x+1}{2009}+1\right)=0$ $\Leftrightarrow\frac{x+2010}{2006}+\frac{x+2010}{2007}-\frac{x+2010}{2008}-\frac{x+2010}{2009}=0$ $\Leftrightarrow\left(x+2010\right).\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$ + TH1: $x+2010=0$$\Leftrightarrow$$x=-2010$ + TH2: $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}=0$ Vì $\hept{\begin{cases}\frac{1}{2006}>\frac{1}{2008}\\frac{1}{2007}>\frac{1}{2009}\end{cases}}$$\Rightarrow$$\frac{1}{2006}+\frac{1}{2007}>\frac{1}{2008}+\frac{1}{2009}$ $\Rightarrow$$\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}>0$ mà $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-2010$3) Ta có: $\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}{75}+\frac{x+1969}{69}$ $\Leftrightarrow\left(\frac{x+1945}{45}-1\right)+\left(\frac{x+1954}{54}-1\right)-\left(\frac{x+1975}{75}-1\right)-\left(\frac{x+1969}{69}-1\right)=0$ $\Leftrightarrow\frac{x+1900}{45}+\frac{x+1900}{54}-\frac{x+1900}{75}-\frac{x+1900}{69}=0$ $\Leftrightarrow\left(x+1900\right).\left(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\right)=0$ + TH1: $x+1900=0$$\Leftrightarrow$$x=-1900$ + TH2: $\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}=0$ Vì $\hept{\begin{cases}\frac{1}{45}>\frac{1}{75}\\frac{1}{54}>\frac{1}{69}\end{cases}}$$\Rightarrow$$\frac{1}{45}+\frac{1}{54}>\frac{1}{75}+\frac{1}{69}$ $\Rightarrow$$\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}>0$ mà $\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-1900$4) Ta có: $\frac{x-99}{5}+\frac{x-97}{7}=\frac{x-95}{9}+\frac{x-93}{11}$ $\Leftrightarrow\left(\frac{x-99}{5}-1\right)+\left(\frac{x-97}{7}-1\right)-\left(\frac{x-95}{9}-1\right)-\left(\frac{x-93}{11}-1\right)=0$ $\Leftrightarrow\frac{x-104}{5}+\frac{x-104}{7}-\frac{x-104}{9}-\frac{x-104}{11}=0$ $\Leftrightarrow\left(x-104\right).\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)=0$ + TH1: $x-104=0$$\Leftrightarrow$$x=104$ + TH2: $\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}=0$ Vì $\hept{\begin{cases}\frac{1}{5}>\frac{1}{7}\\frac{1}{9}>\frac{1}{11}\end{cases}}$$\Rightarrow$$\frac{1}{5}+\frac{1}{7}>\frac{1}{9}+\frac{1}{11}$ $\Rightarrow$$\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}>0$ mà $\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=104$5) Ta có: $\frac{x+2008}{10}+\frac{x+2010}{9}=\frac{x+2012}{8}+\frac{x+2014}{7}$ $\Leftrightarrow\left(\frac{x+2008}{10}+2\right)+\left(\frac{x+2010}{9}+2\right)-\left(\frac{x+2012}{8}+2\right)-\left(\frac{x+2014}{7}+2\right)=0$ $\Leftrightarrow\frac{x+2028}{10}+\frac{x+2028}{9}-\frac{x+2028}{8}-\frac{x+2028}{7}=0$ $\Leftrightarrow\left(x+2028\right).\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}\right)=0$ + TH1: $x+2028=0$$\Leftrightarrow$$x=-2028$ + TH2: $\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}=0$ Vì $\hept{\begin{cases}\frac{1}{10}< \frac{1}{8}\\frac{1}{9}< \frac{1}{7}\end{cases}}$$\Rightarrow$$\frac{1}{10}+\frac{1}{9}< \frac{1}{8}+\frac{1}{7}$ $\Rightarrow$$\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}< 0$ mà $\frac{1}{10}+\frac{1}{9}-\frac{1}{8}-\frac{1}{7}=0$ $\Rightarrow$Phương trình trên vô nghiệmVậy $x=-2028$Chúc bn hok tốt nha

Ngoc Han ♪ · Answer

1 . $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$$\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$Vì : $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0$$\Rightarrow x+1=0$$\Rightarrow x=-1$2 . $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$$\Rightarrow\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)=\left(\frac{x+2}{2008}+1\right)+\left(\frac{x+1}{2009}+1\right)$$\Rightarrow\frac{x+2010}{2006}+\frac{x+2010}{2007}=\frac{x+2010}{2008}+\frac{x+2010}{2009}$$\Rightarrow\left(x+2010\right)\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$Vì $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\ne0$$\Rightarrow x+2010=0$$\Rightarrow x=-2010$Câu trả lời: 1 . $\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}$$\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0$Vì : $\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0$$\Rightarrow x+1=0$$\Rightarrow x=-1$2 . $\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}$$\Rightarrow\left(\frac{x+4}{2006}+1\right)+\left(\frac{x+3}{2007}+1\right)=\left(\frac{x+2}{2008}+1\right)+\left(\frac{x+1}{2009}+1\right)$$\Rightarrow\frac{x+2010}{2006}+\frac{x+2010}{2007}=\frac{x+2010}{2008}+\frac{x+2010}{2009}$$\Rightarrow\left(x+2010\right)\left(\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\right)=0$Vì $\frac{1}{2006}+\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}\ne0$$\Rightarrow x+2010=0$$\Rightarrow x=-2010$

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