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Vì \(\left|2x-27\right|\ge0\Rightarrow\left|2x-27\right|^{2011}\ge0\); \(\left(3y+10\right)^{2012}\ge0\)
=>\(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}\ge0\)
Dấu "=" xảy ra khi \(\left|2x-27\right|^{2011}=\left(3y+10\right)^{2012}=0\Leftrightarrow\hept{\begin{cases}\left|2x-27\right|=0\\\left(3y+10\right)^{2012}=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x-27=0\\3y+10=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{27}{2}\\y=-\frac{10}{3}\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Vì \(\left\{{}\begin{matrix}\left|2x-27\right|^{2011}\text{≥0,∀x}\\\left(3y+10\right)^{2012}\text{≥0,∀y}\end{matrix}\right.\)
⇒ \(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}\text{≥0,∀x},y\)
Dấu "=" ⇔ \(\left\{{}\begin{matrix}2x-27=0\\3y+10=0\end{matrix}\right.\)
⇒ \(\left\{{}\begin{matrix}x=\dfrac{27}{2}\\y=-\dfrac{10}{3}\end{matrix}\right.\)
Vậy ...
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\hept{\begin{cases}\left|2x-27\right|^{2011}\ge0\forall x\\\left(3y+10\right)^{2022}\ge0\forall y\end{cases}}\Rightarrow\left|2x-27\right|^{2011}+\left(3y+10\right)^{2022}\ge0\forall x;y\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}2x-27=0\\3y+10=0\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{27}{2}\\y=-\frac{10}{3}\end{cases}}\)
Vậy x = 27/2 ; y = -10/3 là giá trị cần tìm
ta có |2x-27| > hoặc = 0=> |2x-27|^2011> hoặc = 0
(3y+10)^2012> hoặc 0 mà |2x-27|^2011+(3y+10)^2012=0
=>2x-27=0 hoặc 3y+10=0=>2x=27 hoặc 3y=-10
=>x=13,5 hoặc x=-10/3
vậy .............................
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left\{{}\begin{matrix}\left|2x-27\right|^{2011}\ge0\\\left(3y+10\right)^{2012}\ge0\end{matrix}\right.\Leftrightarrow\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}\ge0\)
Mà \(\left|2x-27\right|^{2017}+\left(3y+10\right)^{2012}=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left|2x-27\right|^{2011}=0\\\left(3y+10\right)^{2012}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=13,5\\y=\dfrac{-10}{3}\end{matrix}\right.\)
Vậy...
\(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}=0\)
\(\left|2x-27\right|^{2011}\ge0;\left(3y+10\right)^{2012}\ge0\)
Dấu "=" xảy ra khi:
\(\left|2x-27\right|^{2011}=0\)
\(\Rightarrow\left|2x-27\right|=0\Rightarrow2x-27=0\Rightarrow2x=27\Rightarrow x=\dfrac{27}{2}\)
\(\left(3y+10\right)^{2012}=0\)
\(\Rightarrow3y+10=0\Rightarrow3y=-10\Rightarrow y=\dfrac{-10}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tìm các giá trị của x, y thỏa mãn: |2x-27|2011+(3y+10)2012=0
Giải:Vì \(\hept{\begin{cases}\left|2x-27\right|^{2011}\ge0\\\left(3y+10\right)^{2012}\ge0\end{cases}}\)\(\Rightarrow\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}\ge0\)
Kết hợp với giả thiết ta thấy \(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}=0\) nên:
\(\hept{\begin{cases}\left|2x-27\right|^{2011}=0\\\left(3y+10\right)^{2012}=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}2x-27=0\\3y+10=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\frac{27}{2}\\y=-\frac{10}{3}\end{cases}}\)
Vậy x=\(\frac{27}{2}\);y=\(-\frac{10}{3}\) thỏa mãn bài toán
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa lại:
\(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}=0\)
\(\Rightarrow\left|2x-27\right|^{2011}=0\) và \(\left(3y+10\right)^{2012}=0\)
+) \(\left|2x-27\right|^{2011}=0\)
\(\Rightarrow\left|2x-27\right|=0\)
\(\Rightarrow2x-27=0\)
\(\Rightarrow2x=27\)
\(\Rightarrow x=13,5\)
+) \(\left(3y+10\right)^{2012}=0\)
\(\Rightarrow3y+10=0\)
\(\Rightarrow3y=-10\)
\(\Rightarrow y=\frac{-10}{3}\)
Vậy \(x=13,5;y=\frac{-10}{3}\)
Ta có:
\(\left|2x-27\right|^{2011}+\left(3y+10\right)^{2012}=0\)
\(\Rightarrow\left|2x-27\right|^{2011}=0\) và \(\left(2y+10\right)^{2012}=0\)
+) \(\left|2x-27\right|^{2011}=0\)
\(\Rightarrow\left|2x-27\right|=0\)
\(\Rightarrow2x-27=0\)
\(\Rightarrow2x=27\)
\(\Rightarrow x=13,5\)
+) \(\left(2y+10\right)^{2012}=0\)
\(\Rightarrow2y+10=0\)
\(\Rightarrow2y=-10\)
\(\Rightarrow y=-5\)
Vậy \(x=13,5;y=-5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
|2x-27|^2011>0
(3y+10)^2>0
=|2x-27|^2011+(3y+10)^2>0
mà |2x-27|^2011+(3y+10)^2=0
=>|2x-27|^2011=(3y+10)^2=0
+)|2x-27|^2011=0=>2x-27=0=>2x=27=>x=13,5
+)(3y+10)^2=0=>3y+10=0=>3y=-10=>y=-10/3