Tính nhanh: 2014 x 2014 + 2016 x 2012
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bằng 1 thưa bạn
=(2014*2013 +2014+2014-2016) : (2012 +2013*2014)
=(2014*2013 +2012):(2012+2013*2014)
( 2014 x 2015 - 2016 ) : ( 2012 + 2013 x 2014 )
= ( 4058210 - 2016 ) : ( 2012 + 4054182 )
= 4056194 : 4056194
= 1
\(\frac{2012+2013.2014}{2014.2015-2016}=\frac{2012+2013.2014}{2014.\left(2013+2\right)-2016}\)
\(=\frac{2012+22013.2014}{2014.2013+2014.2-2016}\)
\(=\frac{2012+2013.2014}{2014.2013+2028-2016}\)
\(=\frac{2012+2013.2014}{2014.2013+2012}=1\)
\(\frac{2012+2013.2014}{2014.2015-2016}\)
\(=\frac{2012+2013.2014}{2014.\left(2013+2\right)-2016}\)
\(=\frac{2012+2013.2014}{2014.2013+2014.2-2016}\)
\(=\frac{2012}{2014.2-2016}\)
\(=\frac{2012}{4028-2016}\)
\(=\frac{2012}{2012}\)
\(=1\)
\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{x+y+z}\)
\(\Rightarrow\frac{1}{x}+\frac{1}{y}+\frac{1}{z}-\frac{1}{x+y+z}=0\)
\(\Leftrightarrow\frac{yz\left(x+y+z\right)+xz\left(x+y+z\right)+xy\left(x+y+z\right)-xyz}{xyz\left(x+y+z\right)}=0\)
\(\Leftrightarrow\)\(xyz+y^2z+yz^2+x^2z+xyz+xz^2+x^2y+xy^2+xyz-xyz=0\)
\(\Leftrightarrow\)\(\left(xyz+y^2z\right)+\left(xyz+x^2z\right)+\left(xz^2+yz^2\right)+\left(xy^2+x^2y\right)=0\)
\(\Leftrightarrow yz\left(x+y\right)+xz\left(x+y\right)+z^2\left(x+y\right)+xy\left(x+y\right)=0\)
\(\Leftrightarrow\left(x+y\right)\left(yz+xz+xy+z^2\right)=0\)
\(\Leftrightarrow\left(x+y\right)\left(x+z\right)\left(y+z\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+y\\x+z=0\end{cases}}=0\) hoặc y+z=0
Do đó ta có B=0
2012 + 2013 x 2014 / 2014 x 2015 -2016 = 1
mình trả lời đầu tiên nha
\(2014^2+\left(2014+2\right)\left(2014-2\right)=2014^2+2014^2-4=2\times2014^2-4\)
2014 x2014+2016 x 2012
=2014+2016 x 2012
=(2014+2016) x 2012
=2012 x 4036
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ah hihihi do ngoc