=2012²⁰¹¹-2012.2012²⁰¹⁰+2012.2012²⁰⁰⁹-.......................-2012.2012²-1

còn lại tự làm nhá

ko co ai tra loi ak.hhaa.

1: \(Q=x^2+100x+2500-1500\)

\(=\left(x+50\right)^2-1500>=-1500\)

Dấu '=' xảy ra khi x=-50

2: \(=a^2+2\cdot a\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{7}{4}=\left(a+\dfrac{3}{2}\right)^2+\dfrac{7}{4}>=\dfrac{7}{4}\)

Dấu '=' xảy ra khi a=-3/2

3: \(=-\left(x^2-2x+1-1\right)=-\left(x-1\right)^2+1< =1\)

Dấu '=' xảy ra khi x=1

x=2012

nên x+1=2013

\(f\left(x\right)=x^{2013}-x^{2012}\left(x+1\right)+x^{2011}\left(x+1\right)-...+x\left(x+1\right)-1\)

\(=x^{2013}-x^{2013}-x^{2012}+x^{2012}+x^{2011}-...+x^2+x+1\)

=x+1=2013

\(\dfrac{x+4}{2011}+\dfrac{x+3}{2012}=\dfrac{x+2}{2013}+\dfrac{x+1}{2014}\)

\(\Rightarrow\dfrac{x+4}{2011}+1+\dfrac{x+3}{2012}+1=\dfrac{x+2}{2013}+1+\dfrac{x+1}{2014}+1\)

\(\Rightarrow\dfrac{x+2015}{2011}+\dfrac{x+2015}{2012}-\dfrac{x+2015}{2013}-\dfrac{x+2015}{2014}=0\)

\(\Rightarrow\left(x+2015\right)\left(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2013}-\dfrac{1}{2014}\right)=0\)

Mà \(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2013}-\dfrac{1}{2014}\ne0\)

\(\Rightarrow x+2015=0\Rightarrow x=-2015\)

Vậy x = -2015

\(\dfrac{x+4}{2011}+\dfrac{x+3}{2012}+\dfrac{x+2}{2013}+\dfrac{x+1}{2014}\)

\(\Rightarrow\dfrac{x+4}{2011}+\dfrac{x+3}{2012}-\dfrac{x+2}{2013}-\dfrac{x+1}{2014}=0\)

\(\Rightarrow\)\(\left(\dfrac{x+4}{2011}+1\right)+\left(\dfrac{x+3}{2012}+1\right)-\left(\dfrac{x+2}{2013}+1\right)-\left(\dfrac{x+1}{2014}+1\right)=0\)\(\Rightarrow\dfrac{x+2015}{2011}+\dfrac{x+2015}{2012}-\dfrac{x+2015}{2013}-\dfrac{x+2015}{2014}=0\)

\(\Rightarrow\left(x+2015\right)\left(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2013}-\dfrac{1}{2014}\right)=0\)

\(\Rightarrow x+2015=0\Rightarrow x=-2015\)

a, Đ/k x-2012>=0 suy ra x>=2012

|x-2011|=\(\orbr{\begin{cases}x-2012\\2012-x\end{cases}}\)

TH1:x-2011=x-2012

suy ra 0=4023(loại vì mất x)

TH2: x-2011=2012-x

suy ra 2x=4023

suy ra x=2011,5

Vậy..........

k o  b i ế t  n h a