Cho P=1-\(\left[\frac{2x-1+\sqrt{x}}{1-\sqrt{x}}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right]\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
a, Rút gọn P
b, Tìm x thuộc Z để P thuộc Z
Cho x,y,z>0 thỏa mãn \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}+\sqrt{z}=2\\x+y+z=2\end{matrix}\right.\)
Tính P=\(\sqrt{\left(x+1\right)\left(y+1\right)\left(z+1\right)}\left(\frac{\sqrt{x}}{x+1}+\frac{\sqrt{y}}{y+1}+\frac{\sqrt{z}}{z+1}\right)\)
Cho a,b,c>0 thỏa a+b+c=3. Tìm Max P \(\frac{2}{3+ab+bc+ca}+\frac{\sqrt{abc}}{6} +\sqrt[3]{\frac{abc}{\left(1+a\right)\left(1+b\right)\left(1+c\right)}}\)
Cho x,y,z>0 thỏa \(3x+y+z=x^2+y^2+z^2+2xy\) . Tìm Min P= \(\frac{20}{\sqrt{x+2}}+\frac{20}{\sqrt{y+2}}+x+y+z\)
Cho biểu thức \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
a)Rút gọn P
b)Tìm x để \(P< \frac{1}{2}\)
c)Tìm x để \(P.\left(\sqrt{x}+3\right)+2\sqrt{x}-2+x=2\)
d)Tìm m để \(P.\left(\sqrt{x}+3\right)+x\left(\sqrt{x}-m\right)=x-\sqrt{x}\left(3+m\right)\)
\(\left(\sqrt{\left(\sqrt{20}\right)-\sqrt{19}}\right)^x+\left(\sqrt{\left(\sqrt{20}\right)+\sqrt{19}}\right)^x=2\)
Cho x,y,z>0 /xyz=8.
Tìm min P= \(\dfrac{x^2}{\sqrt{\left(1+x^3\right)\left(1+y^3\right)}}+\dfrac{y^2}{\sqrt{\left(1+y^3\right)\left(1+z^3\right)}}+\dfrac{z^2}{\sqrt{\left(1+z^3\right)\left(1+x^3\right)}}\)
Cho biểu thức : \(A=\left(\frac{x-3\sqrt{x}}{x-9}-1\right):\left(\frac{9-x}{x+\sqrt{x}-6}+\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}+3}\right)\)
a, Rút gọn A
b, Tìm x để A < 1
c, Tìm \(x\in Z\) để \(A\in Z\)
\(A=\left(\frac{x+\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}+\frac{1}{x+1}\right):\left(\frac{1}{\sqrt{x}-1}-\frac{2\sqrt{x}}{x\sqrt{x}-x+\sqrt{x}-1}\right)\)
a)Rút gọn
b)Tìm x để A=\(1+\frac{2\sqrt{3}}{3}\)
c)Tìm x để A\(\in\) Z
Cho biểu thức:
\(P=\left(\frac{2\sqrt{x}}{\sqrt{x+3}}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
a)Rút gọn biểu thức P
b)Tìm x để \(p< -\frac{1}{2}\)
c)Tìm x để \(P.\left(\sqrt{x}+3\right)+2\sqrt{x}-2+x=2\)
d)Tìm m để \(P.\left(\sqrt{x}+3\right)+x\left(\sqrt{x}-m\right)=x-\sqrt{x}\left(3+m\right)\)
