\(\left(x-2011\right)^{x+1}-\left(x-2011\right)^{x+2011}=0\)
\(\Rightarrow\left(x-2011\right)^{x+1}.\left(1-x^{2010}\right)=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}\left(x-2011\right)^{x+1}=0\\1-x^{2010}=0\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=2011\\x=\pm1\end{array}\right.\)
Vậy x = 2011 ; x = 1 ; x = - 1
Tìm x biết :
( x - 2011)x+1 - ( x - 2011 )x+2011 = 0
1, tìm x biết 2011-|x-2011|=x
tìm x biết a)\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)
b)\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
Tìm x biết: x+1/2013 + x+2/2012 + x+3/2011 = -3
a/ Cho x,y,z khác 0 thỏa mãn \(\frac{y+z-x}{x}=\frac{z+x-y}{y}=\frac{x+y-z}{z}\)
tính B=\(\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\)
b/ Cho a,b,c,d khác 0. Tính
\(T=x^{2011}+y^{2011}+z^{2011}+t^{2011}\) biết x,y,z,t thỏa mãn :
\(\frac{x^{2010}+y^{2010}+z^{2010}+t^{2010}}{a^2+b^2+c^2+=d^2}=\frac{x^{2010}}{a^2}+\frac{y^{2010}}{b^2}+\frac{z^{2010}}{c^2}+\frac{t^{2010}}{d^2}\)
Tìm x biết: //x-2010/-1/=2011
Tìm số hữu tĩ x, biết :\(\frac{x+4}{2011}+\frac{x+3}{2012}=\frac{x+2}{2013}+\frac{x+1}{2014}\)
\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}+\frac{1}{2011}\)
Tìm x
tìm x biết:
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right).503x\)\(=\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)