tìm x để P đạt GTNN
P= cănx -1 phần cănx+2
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28 tháng 6 2017
a.ĐKXĐ;\(\hept{\begin{cases}x\ge0\\x\ne4\end{cases}}\)
b.P=\(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)=\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)-2-5\sqrt{x}}{x-4}\)
=\(\frac{3x-6\sqrt{x}}{x-4}=\frac{3\sqrt{x}.\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)=\(\frac{3\sqrt{x}}{\sqrt{x}+2}\)
c.P=2\(\Leftrightarrow\frac{3\sqrt{x}}{\sqrt{x}+2}=2\Leftrightarrow3\sqrt{x}=2\sqrt{x}+\text{4}\)\(\Leftrightarrow\sqrt{x}=4\Leftrightarrow x=16\)
Vậy x=16
11 tháng 8 2023
a) \(P=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{\sqrt{x}}{x-1}\right):\left(\dfrac{x\sqrt{x}-1}{x\sqrt{x}-\sqrt{x}}\right)\)
\(P=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right):\left(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)
\(P=\left(\dfrac{\sqrt{x}+1+x}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\right):\dfrac{x+\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(P=\dfrac{x+\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}\)
\(P=\dfrac{1}{\sqrt{x}-1}\)
b) P = \(\dfrac{1}{2}\) khi:
\(\dfrac{1}{\sqrt{x}-1}=\dfrac{1}{2}\)
\(\Rightarrow2=\sqrt{x}-1\)
\(\Rightarrow\sqrt{x}=3\)
\(\Rightarrow x=9\left(tm\right)\)
11 tháng 8 2023
a: \(P=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{\sqrt{x}}{x-1}\right):\dfrac{x\sqrt{x}-1}{x\sqrt{x}-\sqrt{x}}\)
\(=\dfrac{\sqrt{x}+1+x}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(x-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{1}{\sqrt{x}-1}\)
b: P=1/2
=>căn x-1=2
=>căn x=3
=>x=9
NH
0
\(P=\dfrac{\sqrt{x}+2-3}{\sqrt{x}+2}=1-\dfrac{3}{\sqrt{x}+2}\)
\(\sqrt{x}+2>=2\)
=>\(\dfrac{3}{\sqrt{x}+2}< =\dfrac{3}{2}\)
=>\(-\dfrac{3}{\sqrt{x}+2}>=-\dfrac{3}{2}\)
=>\(P=\dfrac{-3}{\sqrt{x}+2}+1>=-\dfrac{3}{2}+1=-\dfrac{1}{2}\)
Dấu = xảy ra khi x=0