giúp với ( ai giúp được mình tích cho nha) và làm quen lun tìm x biết \(\frac{x+4}{2009}+\frac{x+3}{2010}=\frac{x+2}{2011}\frac{x+1}{2012}\)
Tìm x, biết:
\(\frac{x+1}{2013}+\frac{x}{2012}+\frac{x-1}{2011}=\frac{x-2}{2010}+\frac{x-3}{2009}+\frac{x-4}{2008}\)
Giúp mk nha các bn! Tks trc!
\(\frac{x+1}{2013}+\frac{x}{2012}+\frac{x-1}{2011}=\frac{x-2}{2010}+\frac{x-3}{2009}+\frac{x-4}{2008}\)
\(\Leftrightarrow\frac{x+1}{2013}-1+\frac{x}{2012}-1+\frac{x-1}{2011}-1=\frac{x-2}{2010}-1+\frac{x-3}{2009}-1+\frac{x-4}{2008}-1\)
\(\Leftrightarrow\frac{x-2012}{2013}+\frac{x-2012}{2012}+\frac{x-2012}{2011}=\frac{x-2012}{2010}+\frac{x-2012}{2009}+\frac{x-2012}{2008}\)
\(\Leftrightarrow\frac{x-2012}{2013}+\frac{x-2012}{2012}+\frac{x-2012}{2011}-\frac{x-2012}{2010}-\frac{x-2012}{2009}-\frac{x-2012}{2008}=0\)
\(\Leftrightarrow\left(x-2012\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)
\(\Leftrightarrow x-2012=0\). Do \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\ne0\)
\(\Leftrightarrow x=2012\)
Giúp mình với: Tìm x ; y ;z
\(\frac{\sqrt{x-2009}-1}{x-2009}+\frac{\sqrt{y-2010}-1}{y-2010}+\frac{\sqrt{z-2011}}{z-2011}=\frac{3}{4}\)
Tìm số hữu tỉ x biết:
a) \(\frac{x+4}{2009}+\frac{x+3}{2010}=\frac{x+2}{2011}+\frac{x+1}{2012}\)
b) \(\frac{x-2011}{2010}+\frac{x-2011}{2011}+\frac{x-2011}{2012}=\frac{x-2011}{2013}+\frac{x-2011}{2014}\)
a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)
\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)
\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)
\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\) (1)
Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)
Nên biểu thức (1) xảy ra khi \(x+2013=0\)
\(x=-2013\)
b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\) (2)
Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)
Nên biểu thức (2) xảy ra khi \(x-2011=0\)
\(x=2011\)
Tìm x biết :
\(\frac{x-1}{2012}+\frac{x-2}{2011}+\frac{x-3}{2010}+\frac{x-4}{2009}+\frac{x-2021}{2}=0\)
Ta có :
\(\frac{x-1}{2012}+\frac{x-2}{2011}+\frac{x-3}{2010}+\frac{x-4}{2009}+\frac{x-2021}{2}=0\)
\(\Leftrightarrow\)\(\left(\frac{x-1}{2012}-1\right)+\left(\frac{x-2}{2011}-1\right)+\left(\frac{x-3}{2010}-1\right)+\left(\frac{x-4}{2009}-1\right)+\left(\frac{x-2021}{2}+4\right)=0\)
\(\Leftrightarrow\)\(\frac{x-2013}{2012}+\frac{x-2013}{2011}+\frac{x-2013}{2010}+\frac{x-2013}{2009}+\frac{x-2013}{2}=0\)
\(\Leftrightarrow\)\(\left(x-2013\right)\left(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2}\right)=0\)
Vì \(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2}\ne0\)
Nên \(x-2013=0\)
\(\Rightarrow\)\(x=2013\)
Vậy \(x=2013\)
Chúc bạn học tốt ~
Bài toán này mình đã làm được rồi,bao nhiêu bạn làm được bài này?
Tìm x có giá trị nguyên biết:\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{x+4}{2011}+\frac{x+5}{2010}+\frac{x+6}{2009}\)
Các bạn làm đầy đủ cả lời giải nha.Mình sẽ k cho bạn nào nhanh nhất!
Ta có: \(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{x+4}{2011}+\frac{x+5}{2010}+\frac{x+6}{2009}\)
\(\Rightarrow\frac{x+1}{2014}+1+\frac{x+2}{2013}+1+\frac{x+3}{2012}+1=\frac{x+4}{2011}+1+\frac{x+5}{2010}+1+\frac{x+6}{2009}+1\)
\(\Rightarrow\frac{2015+x}{2014}+\frac{2015+x}{2013}+\frac{2015+x}{2012}=\frac{2015+x}{2011}+\frac{2015+x}{2010}+\frac{2015+x}{2009}\)
\(\Rightarrow\left(2015+x\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}\right)=0\)
=> 2015 + x = 0
=> x = -2015
Các bạn check lại ở dáp án của Ngọc Vĩ nhé!
Giải phương trình \(\frac{x-1}{2012}+\frac{x-2}{2011}+\frac{x-3}{2010}+................+\frac{x-2012}{1}=2012\)
Giúp mik nha ai nhanh nhất mik tik
\(\Leftrightarrow\left(\frac{x-1}{2012}-1\right)+\left(\frac{x-2}{2011}-1\right)+...+\left(\frac{x-2012}{1}-1\right)=0\)
\(\Leftrightarrow\frac{x-2013}{2012}+\frac{x-2013}{2011}+...+\frac{x-2013}{1}=0\)
\(\Leftrightarrow\left(x-2013\right)\left(\frac{1}{2012}+\frac{1}{2011}+....+1\right)=0\)
\(\Leftrightarrow x-2013=0\)(because 1/2012 +1/2011+...+1 luôn lớn hơn 0
\(\Leftrightarrow x=2013\)
Vậy ........
tìm x biết
\(\frac{x+2}{2012}+\frac{x+3}{2011}+\frac{x+4}{2010}+\frac{x+5}{2009}\)
Tìm x biết \(\frac{x+2}{2012}+\frac{x+3}{2011}=\frac{x+4}{2010}+\frac{x+5}{2009}\)
\(\frac{x+2}{2012}+\frac{x+3}{2011}=\frac{x+4}{2010}+\frac{x+5}{2009}\)
\(\Rightarrow\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=\frac{x+4}{2010}+1+\frac{x+5}{2009}+1\)
\(\frac{x+2}{2012}+\frac{2012}{2012}+\frac{x+3}{2011}+\frac{2011}{2011}=\frac{x+4}{2010}+\frac{2010}{2010}+\frac{x+5}{2009}+\frac{2009}{2009}\)
\(\frac{x+2014}{2012}+\frac{x+2014}{2011}=\frac{x+2014}{2010}+\frac{x+2014}{2009}\)
\(\frac{x+2014}{2012}+\frac{x+2014}{2011}-\frac{x+2014}{2010}-\frac{x+2014}{2009}=0\)
\(\left(x+2014\right)\left(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}\right)=0\)
mà \(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}\ne0\)
nên \(x+2014=0\)
\(x=-2014\)
Giúp mình với:
Giải phương trình :
\(\frac{\sqrt{x-2009}-1}{x-2009}+\frac{\sqrt{y-2010}-1}{y-2010}+\frac{\sqrt{z-2011}}{z-2011}=\frac{3}{4}\)
tham khảo Câu hỏi của Đỗ Thu Hà - Toán lớp 9 - Học toán với OnlineMath
ĐKXĐ:x≠2009;y≠2010;z≠2011;x,y,z∈R
√x−2009−1x−2009 +√y−2010−1y−2010 +√z−2011−1z−2011 =3/4⇔1x−2009 −√x−2009x−2009 +1y−2010 −√y−2011y−2011 +1z−2011 −√z−2011z−2011 =−34⇔(1√x−20092 −1√x−2009 +14 )+(1√y−20102 −1√y−2010 +14 )+(1√z−20112 +1√z−2011 +14 )=0⇔(1√x−2009 −12 )2+(1√y−2010 −12 )2+(1√z−2011 −12 )2=0
k cho mk nha
mk nhanh nhất