Câu 27: B

Câu 26: D

Câu 25: A

Câu 24: \(A=\frac{x+2}{x\cdot\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}\)

\(=\frac{x+2+\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

\(=\frac{x+2+x-1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}}{x+\sqrt{x}+1}\)

\(A-\frac13=\frac{\sqrt{x}}{x+\sqrt{x}+1}-\frac13=\frac{3\sqrt{x}-x-\sqrt{x}-1}{3\left(x+\sqrt{x}+1\right)}\)

\(=\frac{-x+2\sqrt{x}-1}{3\left(x+\sqrt{x}+1\right)}=\frac{-\left(\sqrt{x}-1\right)^2}{3\left(x+\sqrt{x}+1\right)}<0\forall x\) thỏa mãn ĐXKĐ

=>A<1/3

=>Chọn B

Câu 22:

\(P=\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)\left(\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}\right)^2\)

\(=\frac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\left(\frac{1-x}{2\sqrt{x}}\right)^2\)

\(=\frac{x-2\sqrt{x}-1-x-2\sqrt{x}-1}{x-1}\cdot\frac{\left(1-x\right)^2}{4x}=\frac{-4\sqrt{x}}{4x}\cdot\left(x-1\right)=-\frac{x-1}{\sqrt{x}}\)

\(P>2\sqrt{x}\)

=>\(\frac{-x+1}{\sqrt{x}}>2\sqrt{x}\)

=>\(-x+1>2x\)

=>-3x>-1

=>x<1/3

=>0<x<1/3

=>Chọn D

mn giúp em vs ạ em cần gấp cảm ơn ạ 

\(∘ backwin\)

\(CD:1 × 4 = 4 ( c m )\)

\(CR:1 × 3 = 3 ( c m )\)

\(Chiều\) \(cao:1 × 4 = 4 ( c m )\)

\(V: 4 × 3 × 4 = 48 ( c m ^3 )\)

\(Đ/s:48cm^3\)

cảm ơn bạn

giúp mình câu c câu d với

3.

a, \(\sqrt{18x}=3\sqrt{2x}\)

b, \(\sqrt{75x^2y}=5\left|x\right|\sqrt{3y}\)

c, \(11\left|xy\right|\sqrt{5x}\)

giúp mình câu 4 ,5 dc ko ạ ??

Pt có 2 nghiệm khi: \(\left\{{}\begin{matrix}m\ne0\\\Delta'=9\left(m-1\right)^2-9m\left(m-3\right)\ge0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}m\ne0\\m\ge-1\end{matrix}\right.\)

Khi đó theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{6\left(m-1\right)}{m}\\x_1x_2=\dfrac{9\left(m-3\right)}{m}\end{matrix}\right.\)

\(x_1+x_2=x_1x_2\Rightarrow\dfrac{6\left(m-1\right)}{m}=\dfrac{9\left(m-3\right)}{m}\)

\(\Rightarrow6\left(m-1\right)=9\left(m-3\right)\)

\(\Rightarrow m=7\)

A đúng

Dạ em cảm ơn nhiều ạ!

Chọn 

Bài 2: 

Ta có: \(3n^3+10n^2-5⋮3n+1\)

\(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)

\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

\(\Leftrightarrow3n\in\left\{0;-3;3\right\}\)

hay \(n\in\left\{0;-1;1\right\}\)