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Sao mấy bạn không tìm 1 hướng giải khác tốt hơn nhỉ ??? Ví dụ như so sánh với số trung gian
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Ta thấy :
\(\frac{-13}{38}< \frac{-13}{39}=\frac{-1}{3}=\frac{-29}{87}< \frac{-29}{88}\)
Vậy \(\frac{-13}{38}< \frac{-29}{88}\)
\(\frac{x+2}{2018}+\frac{x+3}{2017}+\frac{x+4}{2016}=-3\)
\(\Rightarrow\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)+\left(\frac{x+4}{2016}+1\right)=0\)
\(\Rightarrow\frac{x+2020}{2018}+\frac{x+2020}{2017}+\frac{x+2020}{2016}=0\)
\(\Rightarrow\left(x+2020\right).\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)
\(\Rightarrow x+2020=0\Rightarrow x=2020\)
\(\frac{x-1}{2000}+\frac{x-3}{1998}+\frac{x-5}{1996}+\frac{x}{667}=6\)
\(\Rightarrow\frac{x-1}{2000}+\frac{x-3}{1998}+\frac{x-5}{1996}+\frac{x}{667}-6=0\)
\(\Rightarrow\left(\frac{x-1}{2000}-1\right)+\left(\frac{x-3}{1998}+1\right)+\left(\frac{x-5}{1996}-1\right)+\left(\frac{x}{667}-3\right)=0\)
\(\Rightarrow\frac{x-1-2000}{2000}+\frac{x-3-1998}{1998}+\frac{x-5-1996}{1996}+\frac{x-3.667}{667}=0\)
\(\Rightarrow\frac{x-2001}{2000}+\frac{x-2001}{1998}+\frac{x-2001}{1996}+\frac{x-2001}{667}=0\)
\(\Rightarrow\left(x-2001\right)\left(\frac{1}{2000}+\frac{1}{1998}+\frac{1}{1996}+\frac{1}{667}\right)=0\)
Ta có: \(\frac{1}{2000}+\frac{1}{1998}+\frac{1}{1996}+\frac{1}{667}\ne0\)
\(\Rightarrow x-2001=0\Rightarrow x=2001\)
Đặt 2020=a; 2021=b; 2022=c, ta có :
\(\frac{bx-ay}{c}=\frac{az-cx}{b}=\frac{cy-bz}{a}\)
Theo tính chất của dãy tỉ số bằng nhau, ta có:
\(\frac{bx-ay}{c}=\frac{az-cx}{b}=\frac{cy-bz}{a}=\frac{bcx-acx}{c^2}=\frac{abz-cbx}{b^2}=\frac{acy-abz}{a^2}=\frac{bcx-acx+abz-bcx+acy-abz}{a^2+b^2+c^2}=0\)
\(\Rightarrow\hept{\begin{cases}\frac{bx-ay}{c}=0\\\frac{az-cx}{b}=0\\\frac{cy-bz}{a}=0\end{cases}}\Leftrightarrow\hept{\begin{cases}bx-ay=0\\az-cx=0\\cy-bz=0\end{cases}}\Leftrightarrow\hept{\begin{cases}ay=bx\\az=cx\\cy=bz\end{cases}}\)
Thay 2020=a; 2021=b; 2022=c, ta có :
\(\hept{\begin{cases}2020y=2021x\\2020z=2022x\\2022y=2021z\end{cases}}\Rightarrow\hept{\begin{cases}\frac{y}{2021}=\frac{x}{2020}\\\frac{z}{2022}=\frac{x}{2020}\\\frac{y}{2021}=\frac{z}{2022}\end{cases}}\)
\(\Rightarrow\frac{x}{2020}=\frac{y}{2021}=\frac{z}{2022}\)
\(\left|x+3\right|=2x-1\)
\(\Rightarrow\orbr{\begin{cases}x+3=2x-1\\-x-3=2x-1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3+1=2x-x\\-3+1=2x+x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=4\\3x=-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-2}{3}\end{cases}}\)