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1) \(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
2)\(\frac{a-c}{b-d}=\frac{a+c}{b+d}\Rightarrow\frac{a-c}{a+c}=\frac{b-d}{b+d}\)
3) \(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\Rightarrow\frac{a}{a+c}=\frac{b}{b+d}\)
4)\(\frac{a}{b}=\frac{c}{d}=\frac{a-c}{b-d}\Rightarrow\frac{a}{a-c}=\frac{b}{b-d}\)
5)\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\Rightarrow\frac{c}{a+c}=\frac{d}{b+d}\)
6)\(\frac{a}{b}=\frac{c}{d}=\frac{a-c}{b-d}\Rightarrow\frac{c}{a-c}=\frac{d}{b-d}\)
a) \(1-\frac{1}{2}.\left(\frac{3}{2}-2x\right)=4x-\frac{1}{4}\)
\(-4x+\frac{3}{4}+x=1+\frac{1}{4}\)
\(-3x=\frac{4}{4}+\frac{1}{4}-\frac{3}{4}\)
\(-3x=\frac{1}{2}\)
\(x=\frac{-1}{6}\)
vay \(x=\frac{-1}{6}\)
b) \(x^{10}=1024\)
\(x^{10}=2^{10}\)
\(\Rightarrow x=2\)
vay \(x=2\)
c) \(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
vay \(x=4\)
Bài 1:
\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+...+\left|x+\frac{1}{101}\right|=101x\)
Ta thấy:
\(VT\ge0\Rightarrow VP\ge0\Rightarrow101x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{6}\right)+...+\left(x+\frac{1}{101}\right)=101x\)
\(\Rightarrow\left(x+x+...+x\right)+\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{101}\right)=0\)
\(\Rightarrow10x+\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\frac{10}{11}=0\)
\(\Rightarrow10x=-\frac{10}{11}\Rightarrow x=-\frac{1}{11}\)(loại,vì x\(\ge\)0)
Bài 2:
Ta thấy: \(\begin{cases}\left(2x+1\right)^{2008}\ge0\\\left(y-\frac{2}{5}\right)^{2008}\ge0\\\left|x+y+z\right|\ge0\end{cases}\)
\(\Rightarrow\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|\ge0\)
Mà \(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\Rightarrow\begin{cases}\left(2x+1\right)^{2008}=0\\\left(y-\frac{2}{5}\right)^{2008}=0\\\left|x+y+z\right|=0\end{cases}\)\(\Rightarrow\begin{cases}2x+1=0\\y-\frac{2}{5}=0\\x+y+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\x+y+z=0\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{2}+\frac{2}{5}+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{10}=-z\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{1}{10}\end{cases}\)
a\(\frac{a}{b}\)/b=3/5 => a/3=b/5 =>a/12=b/20 (x)
b/c=4/7 => b/4=c/7 =>b/20=c/35 (y)
Từ (x), (y) => a/12=b/20=c/35 và a+b+c=9
Theo T/c dãy tỉ số bằng nhau
a/12=b/20=c/35=a+b+c/12+20+35=9/67
a/12=9/67 => a=108/67
b/20=9/67 => b=180/67
c/35=9/67 => c=315/67
Vậy ...
k nhá
\(\frac{a}{5}=\frac{b}{3};\frac{b}{7}=\frac{c}{4}\)