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Tìm x,y,z biết :
\(\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y-z\right|=0\)
ta có: \(\left(\text{2x − 1}\right)^{2018}\) ≥ 0
\(\left(y-\frac{2}{5}\right)^{2018}\) ≥ 0
\(\left|x+y-z\right|\) ≥ 0
⇒ \(\left(\text{2x − 1 }\right)^{2018}\)+ \(\left(y-\frac{2}{5}\right)^{2018}\) +\(\left|\text{ x + y − z }\right|\) ≥ 0
để \(\left(\text{2x − 1}\right)^{2018}\) + \(\left(y-\frac{2}{5}\right)^{2018}\) + \(\left|\text{x + y − z}\right|\) = 0
⇒ \(\left(\text{2x − 1}\right)^{2018}\) = 0 ⇒ 2x − 1 = 0 ⇒ x = \(\frac{1}{2}\)
\(\left(y-\frac{2}{5}\right)^{2018}\) = 0 ⇒ y − \(\frac{2}{5}\) = 0⇒ \(\frac{2}{5}\)
\(\left|\text{x + y − z}\right|\) = 0 ⇒ x + y − z = 0 ⇒ z = x + y ⇒z = \(\frac{1}{2}\) + \(\frac{2}{5}\) = \(\frac{9}{10}\)
KL: x = \(\frac{1}{2}\); y = \(\frac{2}{5}\); z = \(\frac{9}{10}\)
( mình nghĩ nó còn có nhiều đáp số lắm, nhưng mình ko biết cách làm)
Chúc bạn học có hiệu quả!
a: =>|x-2009|=2009-x
=>x-2009<=0
=>x<=2009
b: =>2x-1=0 và y-2/5=0 và x+y-z=0
=>x=1/2 và y=2/5 và z=x+y=1/2+2/5=5/10+4/10=9/10
(2x-1)2008 \(\ge\) 0 với mọi x
(y-2/5)2008 \(\ge\) 0 với mọi y
|x+y+z| \(\ge\) 0 với mọi x;y;z
=>(2x-1)2008+(y-2/5)2008+|x+y+z| \(\ge\) 0 với mọi x;y;z
Mà (2x-1)2008+(y-2/5)2008+|x+y+z| = 0 (theo đề)
=>(2x-1)2008+(y-2/5)2008=|x+y+z|=0
+)(2x-1)2008=0=>2x-1=0=>2x=1=>x=1/2
+)(y-2/5)2008=0=>y-2/5=0=>y=2/5
+)|x+y+z|=0=>x+y+z=0=>(1/2+2/5)+z=0=>9/10+z=0=>z=-/910
Vậy x=1/2;y=2/5;z=-9/10
\(\left(2x-1\right)^{2008}\ge0\)
\(\left(y-\frac{2}{5}\right)^{2008}\ge0\)
\(\left|x+y+z\right|\ge0\)
\(\Rightarrow\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|\ge0\)
Mà: \(\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\Rightarrow\left(2x-1\right)^{2008}=0;\left(y-\frac{2}{5}\right)^{2008}=0;\left|x+y+z\right|=0\)
\(\Rightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{-9}{10}\end{cases}}\)
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Bài 1:
\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+...+\left|x+\frac{1}{101}\right|=101x\)
Ta thấy:
\(VT\ge0\Rightarrow VP\ge0\Rightarrow101x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{6}\right)+...+\left(x+\frac{1}{101}\right)=101x\)
\(\Rightarrow\left(x+x+...+x\right)+\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{101}\right)=0\)
\(\Rightarrow10x+\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\left(1-\frac{1}{11}\right)=0\)
\(\Rightarrow10x+\frac{10}{11}=0\)
\(\Rightarrow10x=-\frac{10}{11}\Rightarrow x=-\frac{1}{11}\)(loại,vì x\(\ge\)0)
Bài 2:
Ta thấy: \(\begin{cases}\left(2x+1\right)^{2008}\ge0\\\left(y-\frac{2}{5}\right)^{2008}\ge0\\\left|x+y+z\right|\ge0\end{cases}\)
\(\Rightarrow\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|\ge0\)
Mà \(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\left(2x+1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
\(\Rightarrow\begin{cases}\left(2x+1\right)^{2008}=0\\\left(y-\frac{2}{5}\right)^{2008}=0\\\left|x+y+z\right|=0\end{cases}\)\(\Rightarrow\begin{cases}2x+1=0\\y-\frac{2}{5}=0\\x+y+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\x+y+z=0\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{2}+\frac{2}{5}+z=0\end{cases}\)
\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\-\frac{1}{10}=-z\end{cases}\)\(\Rightarrow\begin{cases}x=-\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{1}{10}\end{cases}\)
\(\left(2x-1\right)^{2008}\ge0với\forall x\) mà,\(\left(y-\frac{2}{5}\right)^{2008}\ge0với\forall y\)lại có\(|x+y+z|\ge0với\forall x,y,z\)
\(\Rightarrow\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y+z\right|\ge0với\forall x,y,z\)Dấu ''='' xảy ra khi \(\hept{\begin{cases}2x-1=0\\y-\frac{2}{5}=0\\x+y+z=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\z=-\frac{9}{10}\end{cases}}}\)
\(\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)+\left|x+y+z\right|=0\)
Ta có \(\hept{\begin{cases}\left(2x-1\right)^{2008}\ge0\forall x\\y-\frac{2}{5}\ge0\forall y\\\left|x+y+z\right|\ge0\forall x;y;z\end{cases}}\)
=> \(\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)+\left|x+y+z\right|\ge0\forall x;y;z\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}\left(2x-1\right)^{2008}=0\\y-\frac{2}{5}=0\\\left|x+y+z\right|=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x-1=0\\y=\frac{2}{5}\\x+y+z=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x=1\\y=\frac{2}{5}\\x+y+z=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\x+y+z=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\z=0-\frac{1}{2}-\frac{2}{5}=\frac{-5}{10}-\frac{4}{10}=\frac{-9}{10}\end{cases}}\)
Vậy \(x=\frac{1}{2};y=\frac{2}{5};z=\frac{-9}{10}\)
Học tốt
(2x-1)^2008\(\ge\)0
(y-2/5)^2008\(\ge\)0
|x+y+z|\(\ge\)0
\(\Rightarrow\)(2x-1)^2008+(y-2/5)^2008+|x+y+z|\(\ge\)0
mà (2x-1)^2008+(y-2/5)^2008+|x+y+z|=0
\(\Rightarrow\)(2x-1)^2008=0;(y-2/5)^2008=0;|x+y+z|=0
x=1/2;y=2/5;z=-9/10
\(\left(2x-1\right)^{2008}+\left(y-\dfrac{2}{5}\right)^{2008}+\left|x+y+z\right|=0\)
Nhận xét : \(\left\{{}\begin{matrix}\left(2x-1\right)^{2008}\ge0\forall x\\\left(y-\dfrac{2}{5}\right)^{2008}\ge0\forall y\\\left|x+y+z\right|\ge0\forall x,y,z\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left(2x-1\right)^{2008}=0\\\left(y-\dfrac{2}{5}\right)^{2008}=0\\\left|x+y+z\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{2}{5}\\z=-\dfrac{9}{10}\end{matrix}\right.\)
(2x - 1 )2008+(y - 2/5)2008 + |x + y - z | = 0
=> ( 2x - 1) 2008 =0 => 2x - 1 =0 => 2x = 1 => x = 1/2
( y - 2/5 )2008 = 0 y - 2/5 = 0 y =2/5 y = 2/5
|x + y -z | = 0 x + y - z = 0 x + 2/5 - z = 0 1/2 - 2/5 -z = 0
=>x = 1/2 =>x = 1/2
y = 2/5 y = 2/5
5/10 - 4/10 = z z = 1/ 10
Vậy x = 1/2 ; y = 2/5 : z = 1/10
( nhớ cho mk nha )
ta có: \(\left(2x-1\right)^{2008}\ge0\)
\(\left(y-\frac{2}{5}\right)^{2008}\ge0\)
\(\left|x+y-z\right|\ge0\)
\(\Rightarrow\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y-z\right|\ge0\)
để \(\left(2x-1\right)^{2008}+\left(y-\frac{2}{5}\right)^{2008}+\left|x+y-z\right|=0\)
\(\Rightarrow\left(2x-1\right)^{2008}=0\Rightarrow2x-1=0\Rightarrow x=\frac{1}{2}\)
\(\left(y-\frac{2}{5}\right)^{2008}=0\Rightarrow y-\frac{2}{5}=0\Rightarrow\frac{2}{5}\)
\(\left|x+y-z\right|=0\Rightarrow x+y-z=0\Rightarrow z=x+y\Rightarrow z=\frac{1}{2}+\frac{2}{5}=\frac{9}{10}\)
KL: x= 1/2; y= 2/5; z=9/10
( mk nghĩ nó còn có nhiều đáp số lắm, nhưng mk ko bít cách lm)