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https://dethi.violet.vn/present/showprint/entry_id/11072330
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p/s: nhớ k cho mình nha <3
\(\frac{x-2}{4}=-\frac{16}{2-x}\)
\(\Leftrightarrow\frac{x-2}{4}=\frac{16}{x-2}\)
\(\Leftrightarrow\left(x-2\right)^2=4.16=64\)
\(\Leftrightarrow\left(x-2\right)^2=8^2\)
\(\Leftrightarrow\left(x-2-8\right)\left(x-2+8\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x+6\right)=0\Leftrightarrow\orbr{\begin{cases}x-10=0\\x+6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)
\(\frac{x+2015}{2016}+\frac{x+2016}{2015}+\frac{x+2017}{2014}=-3\)
\(\Leftrightarrow\frac{x+2015}{2016}+1+\frac{x+2016}{2015}+1+\frac{x+2017}{2014}+1=0\)
\(\Leftrightarrow\frac{x+4031}{2016}+\frac{x+4031}{2015}+\frac{x+4031}{2014}=0\)
\(\Leftrightarrow\left(x+4031\right)\left(\frac{1}{2016}+\frac{1}{2015}+\frac{1}{2014}\right)=0\)
Có: \(\frac{1}{2016}+\frac{1}{2015}+\frac{1}{2014}\ne0\)
\(\Rightarrow x+4031=0\)
\(\Rightarrow x=-4031\)
Ta có :
\(x=\frac{2016^{2017}+1}{2016^{2016}+1}\)
\(\frac{1}{2016}x=\frac{2016^{2017}+1}{2016^{2017}+2016}=\frac{2016^{2017}+2016-2015}{2016^{2017}+2016}\)
\(\Rightarrow\frac{1}{2006}x=1-\frac{2015}{2016^{2017}+2016}\)
Ta lại có :
\(y=\frac{2016^{2016}+1}{2016^{2015}+1}\)
\(\Rightarrow\frac{1}{2016}y=\frac{2016^{2016}+1}{2016^{2016}+2016}=\frac{2016^{2016}+2016-2015}{2016^{2016}+2016}\)
\(\Rightarrow\frac{1}{2016}y=1-\frac{2015}{2016^{2016}+2016}\)
Mà \(\frac{2015}{2016^{2017}+2016}< \frac{2015}{2016^{2016}+2016}\)(so sánh mẫu)
\(\Rightarrow1-\frac{2015}{2016^{2017}+2016}>1-\frac{2015}{2016^{2016}+2016}\)
\(\Rightarrow\frac{1}{2016}x>\frac{1}{2016}y\)
\(\Rightarrow x>y\)
DÀI QUÁ KHÔNG TÍNH ĐƯỢC. CÁI NÀY CÓ MÀ ĐI HỎI THẦN ĐỒNG VỀ MÔN TOÁN ĐI
\(\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+2}{2016}+1\right)+\left(\frac{x+1}{2017}+1\right)\)
\(\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2016}+\frac{x+2018}{2017}=0\)
\(x+2018.\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}\right)=0\)
\(\Rightarrow x+2018=0\)
\(\Rightarrow x=-2018\)
\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+2}{2016}+\)\(\frac{x+1}{2017}\)
\(\Rightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+2}{2016}+1\right)+\left(\frac{x+1}{2017}+1\right)\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2016}+\frac{x+2018}{2017}\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2016}-\frac{x+2018}{2017}=0\)
\(\Rightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}\right)=0\)
\(M\text{à:}\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)
\(\Rightarrow x+2018=0\Rightarrow x=-2018\)
Tìm x biết:
\(\frac{x}{2018}+\frac{x+1}{2017}+\frac{x+2}{2016}+\frac{x+3}{2015}=-4\)
Giải:Ta có:\(\frac{x}{2018}+\frac{x+1}{2017}+\frac{x+2}{2016}+\frac{x+3}{2015}=-4\)
\(\Rightarrow\frac{x}{2018}+1+\frac{x+1}{2017}+1+\frac{x+2}{2016}+1+\frac{x+3}{2015}+1=0\)
\(\Rightarrow\frac{x+2018}{2018}+\frac{x+2018}{2017}+\frac{x+2018}{2016}+\frac{x+2018}{2015}=0\)
\(\Rightarrow\left(x+2018\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}\right)=0\)
\(\Rightarrow x+2018=0\) vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}>0\)
\(\Rightarrow x=-2018\)
Vậy x=-2018 thỏa mãn
x2018 +x+12017 +x+22016 +x+32015 =−4
⇒x2018 +1+x+12017 +1+x+22016 +1+x+32015 +1=0
⇒x+20182018 +x+20182017 +x+20182016 +x+20182015 =0
⇒(x+2018)(12018 +12017 +12016 +12015 )=0
⇒x+2018=0 vì 12018 +12017 +12016 +12015 >0
⇒x=−2018
Vậy x=-2018 thỏa mãn
\(\frac{x+2}{2013}+\frac{x+1}{2014}=\frac{x}{2015}+\frac{x-1}{2016}\)
\(\Leftrightarrow\)\(\frac{x+2}{2013}+1+\frac{x+1}{2014}+1=\frac{x}{2015}+1+\frac{x-1}{2016}+1\)
\(\Leftrightarrow\frac{x+2015}{2013}+\frac{x+2015}{2014}=\frac{x+2015}{2015}+\frac{x+2015}{2016}\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}\right)=0\)
Do\(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}>0\)
=>x+2015=0
<=>x=-2015
=> \(\frac{x+2015-2013}{2013}+\frac{x+2015-2014}{2014}=\frac{x+2015-2015}{2015}+\frac{x+2015-2016}{2016}\)
<=> \(\frac{x+2015}{2013}-1+\frac{x+2015}{2014}-1=\frac{x+2015}{2015}-1+\frac{x+2015}{2016}-1\)
<=> \(\frac{x+2015}{2013}+\frac{x+2015}{2014}-\frac{x+2015}{2015}-\frac{x+2015}{2016}=0\)
<=> \(\left(x+2015\right).\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}\right)=0\)
<=> x + 2015 = 0 Vì \(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}\ne0\)
<=> x = -2015
a)
Ta có: \(\frac{x+y}{2014}\ne\frac{x-y}{2016}\)
\(\Leftrightarrow2016x+2016y=2014x-2014y\)
\(\Leftrightarrow2x=-4030y\)
\(\Leftrightarrow x=-2015y\)
Thay \(x=-2015y\)vào \(\frac{x+y}{2014}=\frac{xy}{2015}\)ta được:
\(\Leftrightarrow\frac{-2015+y}{2014}=\frac{-2015y}{2015}\)
\(\Leftrightarrow\frac{-2014y}{2014}=\frac{-2015y^2}{2015}\)
\(\Leftrightarrow-y=-y^2\)
\(\Leftrightarrow y-y^2=0\)
\(\Leftrightarrow y\left(1-y\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y=0\\1-y=0\end{cases}}\Rightarrow\orbr{\begin{cases}y=0\\y=1\end{cases}}\)
Trường hợp \(y=0\):
\(y=0\Rightarrow x.y=-2015.0=0\)
Trường hợp \(y=1\):
\(y=1\Rightarrow x.y=-2015.1=-2015\)