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KC
0
5 tháng 4 2022
1: \(B=\dfrac{\sqrt{x}-1}{\sqrt{x}-2}-\dfrac{5\sqrt{x}-8}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{x-\sqrt{x}-5\sqrt{x}+8}{\sqrt{x}\left(\sqrt{x}-2\right)}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-4\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{\sqrt{x}-4}{\sqrt{x}}\)
2: \(P=A\cdot B=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}\)
\(\Leftrightarrow P-2=\dfrac{x-\sqrt{x}+1}{\sqrt{x}}>0\)
=>P>2
AD
1
PL
10 tháng 7 2023
ĐK: \(x\ge0\)
Lấy P - 1
\(\dfrac{\sqrt{x}-2}{2\sqrt{x}+1}-1\)
\(=\dfrac{\sqrt{x}-2-2\sqrt{x}-1}{2\sqrt{x}+1}\)
\(=\dfrac{-\sqrt{x}-3}{2\sqrt{x}+1}\)
\(=\dfrac{-\left(\sqrt{x}+3\right)}{2\sqrt{x}+1}\)
Ta thấy \(\left\{{}\begin{matrix}\sqrt{x}+3>0\\2\sqrt{x}+1>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-\left(\sqrt{x}+3\right)< 0\\2\sqrt{x}+1>0\end{matrix}\right.\Rightarrow P-1< 0\)
Vậy \(P< 1\).
12 tháng 9 2021
a: Ta có: \(P=\left(\dfrac{x-2\sqrt{x}+4}{\sqrt{x}-2}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}+\dfrac{\sqrt{x}}{\sqrt{x}+2}-\dfrac{x+4}{x-4}\right)\)
\(=\dfrac{x-2\sqrt{x}+4}{\sqrt{x}-2}:\dfrac{x+4\sqrt{x}+4+x-2\sqrt{x}-x-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x-2\sqrt{x}+4}{1}\cdot\dfrac{\sqrt{x}+2}{x+2\sqrt{x}}\)
\(=\dfrac{x-2\sqrt{x}+4}{\sqrt{x}}\)
b: \(P-2=\dfrac{x-4\sqrt{x}+4}{\sqrt{x}}=\dfrac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}}>0\forall x\) thỏa mãn ĐKXĐ
nên P>2
3 tháng 3 2022
a: \(P=\dfrac{x+2+x-1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)
b: Thay x=1/9 vào P, ta được:
\(P=\dfrac{1}{3}:\left(\dfrac{1}{9}+\dfrac{1}{3}+1\right)=\dfrac{1}{3}:\dfrac{1+3+9}{9}=\dfrac{1}{3}\cdot\dfrac{9}{13}=\dfrac{3}{13}\)
MH
17 tháng 10 2023
\(P=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)+\sqrt{x}\left(\sqrt{x}+3\right)-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\dfrac{\sqrt{x}-3}{\sqrt{x}+3}\)
\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\dfrac{\sqrt{x}-3}{\sqrt{x}+3}\)
\(=\dfrac{-3\sqrt{x}-3}{\left(\sqrt{x}+3\right)^2}\)
\(P=-\dfrac{1}{3}\)
\(\Rightarrow\left(\sqrt{x}+3\right)^2=3\sqrt{x}+3\)
\(\Leftrightarrow x-\sqrt{x}+6=0\)
\(\Leftrightarrow\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)=0\)
\(\Leftrightarrow x=9\left(Vì\sqrt{x}+2>0\right)\)
\(P=-\left(\dfrac{3\sqrt{x}+3}{\left(\sqrt{x}+3\right)^2}\right)=-\left(\dfrac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+3\right)^2}\right)< -3< -1\)
T
11 tháng 9 2023
\(P=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+3}{x-9}\left(ĐKXĐ:x\ge0;x\ne9\right)\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\dfrac{3x+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3\sqrt{x}-3}{x-9}\)
\(b,M=P:Q\)
\(=\dfrac{-3\sqrt{x}-3}{x-9}:\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)
\(=\dfrac{-3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(=\dfrac{-3}{\sqrt{x}+3}\)
Ta thấy: \(\sqrt{x}\ge0\forall x\)
\(\Rightarrow\sqrt{x}+3\ge3\forall x\)
\(\Rightarrow\dfrac{1}{\sqrt{x}+3}\le\dfrac{1}{3}\forall x\)
\(\Rightarrow\dfrac{-3}{\sqrt{x}+3}\ge\dfrac{-3}{3}=-1\)
hay \(M\ge-1\)
#Toru
Xét P= \(x+\sqrt{x}\)
Ta có: \(\sqrt{x}\ge0\)và \(x\ge0\)
Suy ra \(x\in N\)
Suy ra khi /P/ thì giá trị vẫn không thay đổi
Vậy P=/P/