giúp mik với mik chuẩn bị phải thi HK

Ta có:\(\left|x-2013\right|+\left|x-2014\right|+\left|y-2015\right|+\left|x-2016\right|\)

\(=\left|x-2013\right|+\left|2016-x\right|+\left|x-2014\right|+\left|y-2015\right|\)

\(\ge\left|x-2013+2016-x\right|+\left|x-2014\right|+\left|y-2015\right|\)

\(=3+\left|x-2014\right|+\left|y-2015\right|\)

\(\ge3+0+0=3\)

Mà \(\left|x-2013\right|+\left|x-2014\right|+\left|y-2015\right|+\left|x-2016\right|=3\)

\(\Rightarrow\) Dấu "=" xảy ra khi và chỉ khi:

\(\hept{\begin{cases}\left(x-2013\right)\left(2016-x\right)\ge0\\\left|x-2014\right|=0\\\left|y-2015\right|=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}2013\le x\le2016\left(1\right)\\x=2014\left(2\right)\\y=2015\end{cases}}\)

Dễ thấy \(\left(2\right)\) thỏa mãn \(\left(1\right)\) nên \(x=2014;y=2015\)

x-y/2014=x+y/2012=x-y+x+y/2014+2012=2x/2026=x/1013 (theo tc dãy tỉ số bằng nhau)

ta lại có: x+y/2012=x.y/2013=x/2013 (chứng minh trên) => y=1

x-y/2014=x.y/2013=x/2013 => x-1/2014=x/2013

thì (x-1).2013=2014x

    2013x-2013=2014x

   -1x=2013 thì x=-2013

Shbh=a x h= 48 x (48 x \(\frac{1}{3}\) ) =768 (cm2 )

1. \(\left(3x-5\right)^{2010}+\left(y-1\right)^{2012}+\left(x-z\right)^{2014}=0\)

Vì \(\left(3x-5\right)^{2010}\ge0\forall x\); \(\left(y-1\right)^{2012}\ge0\forall y\); \(\left(x-z\right)^{2014}\ge0\forall x,z\)

\(\Rightarrow\left(3x-5\right)^{2010}+\left(y-1\right)^{2012}+\left(x-z\right)^{2014}\ge0\)

Dấu " = " xảy ra \(\Leftrightarrow\hept{\begin{cases}3x-5=0\\y-1=0\\x-z=0\end{cases}}\Leftrightarrow\hept{\begin{cases}3x=5\\y=1\\x=z\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{5}{3}\\y=1\\z=\frac{5}{3}\end{cases}}\)

Vậy \(x=z=\frac{5}{3}\)và \(y=1\)