\(\frac{x-1}{2006}+\frac{x-10}{1997}+\frac{x-19}{1988}=3\)
\(\Leftrightarrow\frac{x-2007}{2006}+\frac{x-2007}{1997}+\frac{x-2007}{1988}=0\)
\(\Leftrightarrow x=2007\)
✰ ღ๖ۣۜDαɾƙ ๖ۣۜBαηɠ ๖ۣۜSĭℓεηтღ✰
lắm tắt thế này đi thi ko đc điểm đâu nhóc =))
\(\frac{x-1}{2006}+\frac{x-10}{1997}+\frac{x-19}{1998}=3\)
\(\Leftrightarrow\left(\frac{x-1}{2006}-1\right)+\left(\frac{x-10}{1997}-1\right)+\left(\frac{x-19}{1998}-1\right)=0\)
\(\Leftrightarrow\frac{x-2007}{2006}+\frac{x-2007}{1997}+\frac{x-2007}{1998}=0\)
\(\Leftrightarrow\left(x-2007\right)\left(\frac{1}{2006}+\frac{1}{1997}+\frac{1}{1998}\right)=0\)
Dễ thấy \(\left(\frac{1}{2006}+\frac{1}{1997}+\frac{1}{1998}\right)>0\)nên \(x-2007=0\Leftrightarrow x=2007\)
\(\frac{x-1}{2006}+\frac{x-10}{1997}+\frac{x-19}{1998}=3\)
\(\Rightarrow-1+\frac{x-1}{2006}-1+\frac{x-10}{1997}-1+\frac{x-19}{1988}=0\)
\(\Rightarrow-\frac{x-2007}{2006}-\frac{x-2007}{1997}-\frac{x-2007}{1988}=0\)
\(\Rightarrow-\left(x-2007\right).\left(\frac{1}{2006}+\frac{1}{1997}+\frac{1}{1998}\right)=0\)
\(\Rightarrow-x+2007=0\)
\(\Rightarrow-x=-2007\)
\(\Rightarrow x=2007\)
Study well
\(\frac{x-1}{2006}+\frac{x-10}{1997}+\frac{x-19}{1988}=3\)
\(\Rightarrow\frac{x-1}{2006}+\frac{x-10}{1997}+\frac{x-19}{1988}-3=0\)
\(\Rightarrow\left(\frac{x-1}{2006}-1\right)+\left(\frac{x-10}{1997}-1\right)+\left(\frac{x-19}{1988}-1\right)=0\)
\(\Rightarrow\frac{x-1-2006}{2006}+\frac{x-10-1997}{1997}+\frac{x-19-1988}{1988}=0\)
\(\Rightarrow\frac{x-2007}{2006}+\frac{x-2007}{1997}+\frac{x-2007}{1988}=0\)
Đặt thừa số chung :
\(\left(x-2007\right).\left(\frac{1}{2006}+\frac{1}{1997}+\frac{1}{1998}\right)=0\)
Vì \(\frac{1}{2006}+\frac{1}{1997}+\frac{1}{1998}\ne0\)
\(\Rightarrow x-2007=0\)
\(\Rightarrow x=2007\)
Vậy \(x=2007\)
Chúc bạn học tốt !!!
