(X+Y)^2016+|Y-34|^2018=0
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vì (x-2016)^2016 >= 0 vs mọi x
(y-2017)^2018>= 0 vs mọi y
/x+y-z/ >= 0 vs mọi x,y,z
mà (x-2016)^2016+(y-2017)^2018+/x-y+z/=\(\hept{\begin{cases}\left(x-2016\right)^{2016}=0\\^{\left(-2017\right)^{2018}}=0\\x+y-z=0\end{cases}}\)0 nên \(\hept{\begin{cases}x-2016=0\\y-2017=0\\x+y-z\end{cases}}\)\(\hept{\begin{cases}x=2016\\y=2017\\x+y-z=0\end{cases}}\)
mà x+y=2016+2017=4033
\(\Rightarrow\)4033-z=0
z=4033
vậy x=2016 y=2017 z=4033
![](https://rs.olm.vn/images/avt/0.png?1311)
Vì 2016(x-1)2016 + 2017(y-1)2018 = 0
Mà 2016(x-1)2016 \(\ge\)0 ; 2017(y-1)2018 \(\ge\)0
=> 2016(x-1)2016 = 2017(y-1)2018 =0
=> x-1 = y-1 = 0
=> x=y=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x-2\right)^{2016}+|y^2-9|^{2018}=0\)(*)
Vì \(\left(x-2\right)^{2016}\ge0\)và \(|y^2-9|^{2018}\ge0\)
nên (*)\(\Leftrightarrow\hept{\begin{cases}\left(x-2\right)^{2016}=0\\|y^2-9|^{2018}=0\end{cases}\Leftrightarrow\hept{\begin{cases}x-2=0\\y^2-9=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=2\\\orbr{\begin{cases}y=3\\y=-3\end{cases}}\end{cases}}}}\)
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\(x+y+z=0\Rightarrow\left(x+y+z\right)^2=0\Rightarrow x^2+y^2+z^2+2xy+2yz+2zx=0\)
\(\Rightarrow x^2+y^2+z^2+2\left(xy+yz+zx\right)=0\)
Mà \(xy+yz+zx=0\)(theo đề) nên \(2\left(xy+yz+zx\right)=0\)
\(\Rightarrow x^2+y^2+z^2=0\)
Vì \(\hept{\begin{cases}x^2\ge0\\y^2\ge0\\z^2\ge0\end{cases}}\) (với mọi x;y;z) nên \(x^2+y^2+z^2\ge0\) (với mọi x;y;z)
Để \(x^2+y^2+z^2=0\) \(\Leftrightarrow\) \(\hept{\begin{cases}x^2=0\\y^2=0\\z^2=0\end{cases}\Leftrightarrow}x=y=z=0\)
Vậy \(A=\left(0-1\right)^{2016}+0^{2017}+\left(0+1\right)^{2018}=\left(-1\right)^{2016}+0+1^{2018}=2\)
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1.4m+7n=0
=>4m=-7n
=>mx2-4m=0
=>m(x2-4)=0
=>m=0 hoặc x=2 hoặc x=-2
Vì \(\left(x+y\right)^{2016}\ge0;\left|y-34\right|^{2018}\ge0\)
\(\Rightarrow\left(x+y\right)^{2016}+\left|y-34\right|^{2018}\ge0\)
Dấu "=" xảy ra <=> \(\orbr{\begin{cases}\left(x+y\right)^{2016}=0\\\left|y-34\right|^{2018}=0\end{cases}\Rightarrow\orbr{\begin{cases}x+y=0\\y-34=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=-34\\y=34\end{cases}}}\)