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Vì \(\hept{\begin{cases}\left(\frac{1}{2}x-5\right)^{20}\ge0\\\left(y^2-\frac{1}{4}\right)^{10}\ge0\end{cases}\Rightarrow\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}}\ge0\)
Theo đề bài:
\(\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}\le0\)
=> \(\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}=0\)
<=>\(\hept{\begin{cases}\left(\frac{1}{2}x-5\right)^{20}=0\\\left(y^2-\frac{1}{4}\right)^{10}=0\end{cases}}\)
<=>\(\hept{\begin{cases}\frac{1}{2}x-5=0\\y^2-\frac{1}{4}=0\end{cases}}\)
<=>\(\hept{\begin{cases}\frac{1}{2}x=5\\y^2=\frac{1}{4}\end{cases}}\)
<=>\(x=10\) và \(y=-\frac{1}{4}\) hoặc \(y=\frac{1}{4}\)
Vậy ...
1/2x-5=y2-1/4=0
1/2.x=5 va y2=1/4
x=10 va y=1/2 hoac x=10 va y=-1/2
\(a;x^2+\left(9-\frac{1}{10}\right)^2=0\)
\(\Leftrightarrow x^2+\frac{89^2}{100}=0\)
\(\Leftrightarrow x^2=-\frac{7921}{100}\)
Mà\(x^2\ge0\Rightarrow x\in\varnothing\)
\(\left(x-1\right)^2+\left(y-3\right)^2=0\)
mà \(\left(x-1\right)^2\ge0;\left(y-3\right)^2\ge0\)
nên để: \(\left(x-1\right)^2+\left(y-3\right)^2=0\) thì:
\(x-1=y-3=0\Rightarrow x=1;y=3\)
a)x-1=y-3=0
x=1 va y=3
b)2x-1/2=y+3/2=0
x=1/4 va y=-3/2
c)1/2x-5=y2-1/4=0
1/2.x=5 va y2=1/4
x=10 va y=1/2 hoac x=10 va y=-1/2
a) \(x^2+\left(y-\dfrac{1}{10}\right)^4=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y-\dfrac{1}{10}=0\end{matrix}\right.\)( do \(x^2\ge0,\left(y-\dfrac{1}{10}\right)^4\ge0\))
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=\dfrac{1}{10}\end{matrix}\right.\)
b) \(\left(\dfrac{1}{2}.x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}\le0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{2}x-5=0\\y^2-\dfrac{1}{4}=0\end{matrix}\right.\)( do \(\left(\dfrac{1}{2}x-5\right)^{20}\ge0,\left(y^2-\dfrac{1}{4}\right)^{10}\ge0\))
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{2}x=5\\y^2=\dfrac{1}{4}\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=10\\y=\pm\dfrac{1}{2}\end{matrix}\right.\)
\(a,\Leftrightarrow\left\{{}\begin{matrix}x=0\\y-\dfrac{1}{10}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=\dfrac{1}{10}\end{matrix}\right.\\ b,\left\{{}\begin{matrix}\left(\dfrac{1}{2}x-5\right)^{20}\ge0\\\left(y^2-\dfrac{1}{4}\right)^{10}\ge0\end{matrix}\right.\Leftrightarrow\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}\ge0\)
Mà \(\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}\le0\)
\(\Leftrightarrow\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}=0\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{2}x=5\\y^2=\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=10\\y=\pm\dfrac{1}{2}\end{matrix}\right.\)
Ta có : \(\frac{x+1}{x-4}>0\)
Thì sảy ra 2 trường hợp
Th1 : x + 1 > 0 và x - 4 > 0 => x > -1 ; x > 4
Vậy x > 4
Th2 : x + 1 < 0 và x - 4 < 0 => x < -1 ; x < 4
Vậy x < (-1) .
Ta có : \(\left(x+2\right)\left(x-3\right)< 0\)
Th1 : \(\hept{\begin{cases}x+2< 0\\x-3>0\end{cases}\Rightarrow\hept{\begin{cases}x< -2\\x>3\end{cases}}\left(\text{Vô lý }\right)}\)
Th2 : \(\hept{\begin{cases}x+2>0\\x-3< 0\end{cases}\Rightarrow\hept{\begin{cases}x>-2\\x< 3\end{cases}\Rightarrow}-2< x< 3}\)
Xét \(\left(\frac{1}{2}x-5\right)^{20}\ge0\)
\(\left(y^2-\frac{1}{4}\right)^{10}\ge0\)
\(\Rightarrow\) \(\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}\ge0\)
mà \(\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}=0\)
\(\Leftrightarrow\hept{\begin{cases}\frac{1}{2}x-5=0\\y^2-\frac{1}{4}=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}\frac{1}{2}x=5\\y^2=\frac{1}{4}\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=10\\y=\pm\frac{1}{2}\end{cases}}\)
x=10;y=1/2