Giải BPT
x+1/x-1+x-1/x+1>5/2
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22 tháng 10 2021
\(\Rightarrow\left(x-1\right)^2-\left(2x-3\right)^2=0\\ \Rightarrow\left(x-1-2x+3\right)\left(x-1+2x-3\right)=0\\ \Rightarrow\left(2-x\right)\left(3x-4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)
PS
1
NU
3
13 tháng 4 2021
\(\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-4\right)\left(x-5\right)}+\dfrac{1}{\left(x-5\right)\left(x-6\right)}=\dfrac{1}{10}\)
\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-2}+\dfrac{1}{x-2}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-....+\dfrac{1}{x-5}-\dfrac{1}{x-6}=\dfrac{1}{10}\)
\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-6}=\dfrac{1}{10}\Leftrightarrow\dfrac{x-6-x+1}{\left(x-1\right)\left(x-6\right)}=\dfrac{1}{10}\)
\(\Leftrightarrow x^2-7x+56=0\Leftrightarrow x^2-2.\dfrac{7}{2}x+\dfrac{49}{4}+\dfrac{175}{4}=\left(x-\dfrac{7}{2}\right)^2+\dfrac{175}{4}>0\)
Vậy phương trình vô nghiệm
T
1
MA
14 tháng 9 2016
\(\frac{1}{\left(x+5\right)\left(x+4\right)}+\frac{1}{\left(x+6\right)\left(x+5\right)}+\frac{1}{\left(x+6\right)\left(x+7\right)}=\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+7}=\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+4}-\frac{1}{x+7}=\frac{1}{18}\)
\(\Leftrightarrow\frac{\left(x+7\right)-\left(x+4\right)}{\left(x+7\right)\left(x+4\right)}=\frac{1}{18}\)
\(\Leftrightarrow\frac{3}{x^2+11x+28}=\frac{1}{18}\)
\(\Leftrightarrow x^2+11x+28=54\)
\(\Leftrightarrow x^2+11x=26\)
\(\Leftrightarrow x^2+11x-26=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-13\end{cases}}\)
9 tháng 3 2020
\(\Leftrightarrow\frac{1}{x}+\frac{1}{x+2}+\frac{1}{x+5}+\frac{1}{x+7}-\frac{1}{x+1}-\frac{1}{x+3}-\frac{1}{x+4}-\frac{1}{x+6}=0\)
\(\Leftrightarrow\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}-\frac{1}{\left(x+4\right)\left(x+5\right)}-\frac{1}{\left(x+6\right)\left(x+7\right)}=0\)
\(\Leftrightarrow\frac{8x+20}{x\left(x+1\right)\left(x+4\right)\left(x+5\right)}+\frac{8x+36}{\left(x+2\right)\left(x+3\right)\left(x+6\right)\left(x+7\right)}=0\).Đến đây mk chịu
Giải
\(\frac{x+1}{x-1}+\frac{x-1}{x+1}=\frac{2\left(x+1\right)}{x^2-1}+\frac{2\left(x-1\right)}{x^2-1}=\frac{2\left(x+1\right)+2\left(x-1\right)}{x^2-1}\)
\(\frac{2\left(x+1+x-1\right)}{x^2-1}=\frac{2\left(2x\right)}{x^2-1}=\frac{4x}{x^2-1}\)
Tới đây bí rồi
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