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TN
6 tháng 6 2017
\(\dfrac{x-17}{1997}+\dfrac{x-21}{1993}+\dfrac{x+2}{1008}=4\)
\(\Leftrightarrow\dfrac{x-17}{1997}-1+\dfrac{x-21}{1993}-1+\dfrac{x+2}{1008}-2=0\)\(\Leftrightarrow\dfrac{x-2014}{1997}+\dfrac{x-2014}{1993}+\dfrac{x-2014}{1008}=0\) \(\Leftrightarrow\left(x-2014\right)\left(\dfrac{1}{1993}+\dfrac{1}{1997}+\dfrac{1}{1008}\right)=0\)vì \(\dfrac{1}{1993}+\dfrac{1}{1997}+\dfrac{1}{1008}\ne0\Rightarrow x-2014=0\Rightarrow x=2014\)
2 tháng 4 2020
\(\frac{x+1}{2003}+\frac{x+3}{2001}+\frac{x+5}{1999}=\frac{x+7}{1997}+\frac{x+9}{1995}+\frac{x+11}{1993}\)
\(\Leftrightarrow\frac{x+1}{2003}+1+\frac{x+3}{2001}+1+\frac{x+5}{1999}+1=\frac{x+7}{1997}+1+\frac{x+9}{1995}+1+\frac{x+11}{1993}+1\)
\(\Leftrightarrow\frac{x+2004}{2003}+\frac{x+2004}{2001}+\frac{x+2004}{1999}=\frac{x+2004}{1997}+\frac{x+2004}{1995}+\frac{x+2004}{1993}\)
\(\Leftrightarrow\frac{x+2004}{2003}+\frac{x+2004}{2001}+\frac{x+2004}{1999}-\frac{x+2004}{1997}-\frac{x+2004}{1995}-\frac{x+2004}{1993}=0\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2003}+\frac{1}{2001}+\frac{1}{1999}+\frac{1}{1997}+\frac{1}{1995}+\frac{1}{1993}\right)=0\)
\(\Leftrightarrow x+2004=0\) ( do \(\frac{1}{2003}+\frac{1}{2001}+\frac{1}{1999}+\frac{1}{1997}+\frac{1}{1995}+\frac{1}{1993}\ne0\))
\(\Leftrightarrow x=-2004\)
2 tháng 4 2020
\(\frac{x+1}{2003}\)\(+\)\(\frac{x+3}{2001}\)\(+\)\(\frac{x+5}{1999}\)= \(\frac{x+7}{1997}\)\(+\frac{x+9}{1995}\)\(+\frac{x+11}{1993}\)
\(\Leftrightarrow\)\(\frac{x+1}{2003}\)\(+1+\)\(\frac{x+3}{2001}\)\(+1+\frac{x+5}{1999}\)= \(\frac{x+7}{1997}\)\(+1+\frac{x+9}{1995}\)\(+1+\frac{x+11}{1993}\)
\(\Leftrightarrow\frac{x+2004}{2003}\)\(+\frac{x+2004}{2001}\)\(+\frac{x+2004}{1999}\)\(-\frac{x+2004}{1997}\)\(-\frac{x+2004}{1995}\)\(-\frac{x+2004}{1993}\)\(=0\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2003}+\frac{1}{2001}+\frac{1}{1999}-\frac{1}{1997}-\frac{1}{1995}-\frac{1}{1993}\right)=0\)
\(\Leftrightarrow x+2004=0\)(vì tích kia có kết quả khác 0)
\(\Leftrightarrow x=-2004\)
Vậy PT có tập nghiệm S = {-2004}
19 tháng 4 2020
\(\frac{x+6}{1999}+\frac{x+8}{1997}=\frac{x+10}{1995}+\frac{x+12}{1993}\)
\(\Leftrightarrow\frac{x+6}{1999}+1+\frac{x+8}{1997}+1=\frac{x+10}{1995}+1+\frac{x+12}{1993}+1\)
\(\Leftrightarrow\frac{x+2005}{1999}+\frac{x+2005}{1997}=\frac{x+2005}{1995}+\frac{x+2005}{1993}\)
\(\Leftrightarrow\left(x+2005\right)\left(\frac{1}{1999}+\frac{1}{1997}-\frac{1}{1995}-\frac{1}{1993}\right)=0\)
\(\Leftrightarrow x+2005=0\left(\frac{1}{1999}+\frac{1}{1997}-\frac{1}{1995}-\frac{1}{1993}\ne0\right)\)
<=> x=-2005
Vậy x=-2005
19 tháng 4 2020
bạn chỉ cần cộng mỗi phân số với 1 là xong!
Vd: x+6/1999 +1 +x+8/1997 +1 = x+10/1995 +1 +x+12/1993 +1
(không quen sử dụng cái phần mềm này lắm nên mình không làm nốt được)
ND
1
21 tháng 4 2019
\(\frac{x-17}{1990}+\frac{x-21}{1986}+\frac{x+1}{1004}=4\)
\(\Leftrightarrow\left(\frac{x-17}{1990}-1\right)+\left(\frac{x-21}{1986}-1\right)+\left(\frac{x+1}{1004}-2\right)=0\)
\(\Leftrightarrow\frac{x-2007}{1990}+\frac{x-2007}{1986}+\frac{x-2007}{1004}=0\)
\(\Leftrightarrow\left(x-2007\right)\left(\frac{1}{1990}+\frac{1}{1986}+\frac{1}{1004}\right)=0\)
\(\Leftrightarrow x-2007=0\) (Vì \(\frac{1}{1990}+\frac{1}{1986}+\frac{1}{1004}>0\))
\(\Leftrightarrow x=2007\)
V...
NQ
1
12 tháng 9 2019
\(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-163}{23}=10\)
\(\Leftrightarrow\frac{x-241}{17}-1+\frac{x-220}{19}-2+\frac{x-195}{21}-3+\frac{x-166}{23}-4=0\)
\(\Leftrightarrow\frac{x-258}{17}+\frac{x-258}{19}+\frac{x-258}{21}+\frac{x-258}{23}=0\)
\(\Leftrightarrow\left(x-258\right)\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{23}\right)=0\)
\(\Leftrightarrow x=258\)
Vậy \(x=258\)
Chúc bạn học tốt !!!
\(\frac{x-17}{1997}+\frac{x-21}{1993}+\frac{x+2}{1008}=4\)
\(\Leftrightarrow\frac{x-17}{1997}+\frac{x-21}{1993}+\frac{x+2}{1008}-4=0\)
\(\Leftrightarrow\left(\frac{x-17}{1997}-1\right)+\left(\frac{x-21}{1993}-1\right)+\left(\frac{x+2}{1008}-2\right)=0\)
\(\Leftrightarrow\left(\frac{x-17}{1997}-\frac{1997}{1997}\right)+\left(\frac{x-21}{1993}-\frac{1993}{1993}\right)+\left(\frac{x+2}{1008}-\frac{2016}{1008}\right)=0\)
\(\Leftrightarrow\frac{x-2014}{1997}+\frac{x-2014}{1993}+\frac{x-2014}{1008}=0\)
\(\Leftrightarrow\left(x-2014\right)\left(\frac{1}{1997}+\frac{1}{1993}+\frac{1}{1008}\right)=0\)
\(\Leftrightarrow x-2014=0\)
\(\Leftrightarrow x=2014\)
=.= hok tốt!!