X x 2012 - X = 2012 x 2010 + 2012

X x ( 2012 - 1 ) = 2012 x ( 2010 + 1 )

X x 2011 = 2012 x 2011

\(\Rightarrow\)X = 2012

 X x 2012 - X = 2012 x 2010 + 2012

<=>2011xX=2012x2011

<=>X=2012

~~~~~~~~~~~ai đi ngang qua nhớ để lại k ~~~~~~~~~~~~~

 ~~~~~~~~~~~~ Chúc bạn sớm kiếm được nhiều điểm hỏi đáp ~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~ Và chúc các bạn trả lời câu hỏi này kiếm được nhiều k hơn ~~~~~~~~~~~~

Đặt \(\sqrt{x^2+2012}=t>0\Rightarrow2012=t^2-x^2\)

Pt trở thành:

\(x^4+t=t^2-x^2\)

\(\Leftrightarrow x^4-t^2+x^2+t=0\)

\(\Leftrightarrow\left(x^2+t\right)\left(x^2-t+1\right)=0\)

\(\Leftrightarrow x^2+1=t\)

\(\Leftrightarrow x^2+1=\sqrt{x^2+2012}\)

\(\Leftrightarrow x^4+2x^2+1=x^2+2012\)

\(\Leftrightarrow x^4+x^2-2011=0\)

\(\Leftrightarrow x=\pm\sqrt{\dfrac{-1+\sqrt{8045}}{2}}\)

Ta có :

\(\frac{x-1}{2012}+\frac{x-2}{2011}+\frac{x-3}{2010}+...+\frac{x-2012}{1}=2012\)

\(\Leftrightarrow\)\(\left(\frac{x-1}{2012}-1\right)+\left(\frac{x-2}{2011}-1\right)+\left(\frac{x-3}{2010}-1\right)+...+\left(\frac{x-2012}{1}-1\right)=2012-2012\)

\(\Leftrightarrow\)\(\frac{x-2013}{2012}+\frac{x-2013}{2011}+\frac{x-2013}{2010}+...+\frac{x-2013}{1}=0\)

\(\Leftrightarrow\)\(\left(x-2013\right)\left(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+...+\frac{1}{1}\right)=0\)

Vì \(\left(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+...+1\right)\ne0\)

\(\Rightarrow\)\(x-2013=0\)

\(\Rightarrow\)\(x=2013\)

Vậy \(x=2013\)

Chúc bạn học tốt 

suy ra hai truong hop

1 : x-2011=x-2012

suy ra x-x=2011-2012(loai)

2 : x-2011=-(x-2012)

suy ra : x-2011=-x+2012                                

2x=2011+2012

2x=4023

x=2011.5

kho..................lam............................tich,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,minh..........................troi........................ret............................wa.................ung ho minh.................hu....................hu..............hu................hat..............hat....................s

Cau a biet lam roi de lam cau b cho:

Ta thay:tong 2 so hang do la tong 2 so tu nhien lien tiep nen se la so le (*) ma 2012 la so chan(trai voi "*")

=>Khong ton tai so nguyen x thoa man

Vay khong ton tai so nguyen x thoa man

\(x^4+\sqrt{x^2+2012}=2012.\)

\(\Leftrightarrow x^4=-\sqrt{x^2+2012}+2012.\)

\(\Leftrightarrow x^4+x^2+\frac{1}{4}=x^2+2012-\sqrt{x^2+2012}+\frac{1}{4}.\)

\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2=\left(\sqrt{x^2+2012}-\frac{1}{2}\right)^2.\)

Đến đây chia 2 TH ra là ok

thank nhé

\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2-\left(\sqrt{x^2+2012}-\frac{1}{2}\right)^2=0..\)

HĐT nha hoặc khai phương cx đc