Câu 1: 

a) Ta có: 7x+21=0

\(\Leftrightarrow7x=-21\)

hay x=-3

Vậy: S={-3}

b) Ta có: 3x-2=2x-3

\(\Leftrightarrow3x-2-2x+3=0\)

\(\Leftrightarrow x+1=0\)

hay x=-1

Vậy: S={-1}

c) Ta có: 5x-2x-24=0

\(\Leftrightarrow3x=24\)

hay x=8

Vậy: S={8}

Câu 2: 

a) Ta có: \(\left(2x+1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-1\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=1\end{matrix}\right.\)

Vậy: \(S=\left\{-\dfrac{1}{2};1\right\}\)

b) Ta có: \(\left(2x-3\right)\left(-x+7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\-x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\-x=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=7\end{matrix}\right.\)

Vậy: \(S=\left\{\dfrac{3}{2};7\right\}\)

c) Ta có: \(\left(x+3\right)^3-9\left(x+3\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left[\left(x+3\right)^2-9\right]=0\)

\(\Leftrightarrow\left(x+3\right)\left(x+3-3\right)\left(x+3+3\right)=0\)

\(\Leftrightarrow x\left(x+3\right)\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=-6\end{matrix}\right.\)

Vậy: S={0;-3;-6}

Bài 1: 

a) Ta có: \(P=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{4-x}\)

\(=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\cdot\left(\sqrt{x}+2\right)}+\dfrac{2\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\dfrac{2+5\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)

b)

ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

Để P=2 thì \(\dfrac{3\sqrt{x}}{\sqrt{x}+2}=2\)

\(\Leftrightarrow3\sqrt{x}=2\left(\sqrt{x}+2\right)\)

\(\Leftrightarrow3\sqrt{x}=2\sqrt{x}+4\)

\(\Leftrightarrow3\sqrt{x}-2\sqrt{x}=4\)

\(\Leftrightarrow\sqrt{x}=4\)

hay x=16(nhận)

Vậy: Để P=2 thì x=16

2.

a, \(m=3\), hệ phương trình trở thành:

\(\left\{{}\begin{matrix}x+3y=9\\3x-3y=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4x=13\\y=\dfrac{3x-4}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{13}{4}\\y=\dfrac{23}{12}\end{matrix}\right.\)

b, \(\left(x;y\right)=\left(-1;3\right)\) là nghiệm của hệ, suy ra:

\(\left\{{}\begin{matrix}-1+3m=9\\-m-9=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m=\dfrac{10}{3}\\m=-13\end{matrix}\right.\)

\(\Rightarrow\) Không tồn tại giá trị m thỏa mãn

f: =>(x-3)(x-1)>=0

=>x>=3 hoặc x<=1

g: =>(x-2)(x^2+3)<0

=>x-2<0

=>x<2

h: =>x+2>=0

=>x>=-2

i: =>(x-1-x+3)/(x-3)>0

=>x-3>0

=>x>3

Bài 1: 

a) Ta có: \(2\left(3-4x\right)=10-\left(2x-5\right)\)

\(\Leftrightarrow6-8x-10+2x-5=0\)

\(\Leftrightarrow-6x+11=0\)

\(\Leftrightarrow-6x=-11\)

hay \(x=\dfrac{11}{6}\)

b) Ta có: \(3\left(2-4x\right)=11-\left(3x-1\right)\)

\(\Leftrightarrow6-12x-11+3x-1=0\)

\(\Leftrightarrow-9x-6=0\)

\(\Leftrightarrow-9x=6\)

hay \(x=-\dfrac{2}{3}\)

Đáp án D

Đây là hàm số liên tục trên toàn R và ta có

y 0 = 1 ; y 1 = − 1 ; y 2 = 15 ⇒ y 0 . y 1 < 0 ; y 1 y 2 < 0 ⇒

phương trình có nghiệm trong 0 ; 1 ; 1 ; 2 ⇒  phương trình có ít nhất 2 nghiệm trong 0 ; 2 . 

câu 1 

a) 5x(x-2)=0 =>\(\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

b)(x+5)(2x-7)=0 =>\(\left[{}\begin{matrix}x+5=0\\2x-7=0\end{matrix}\right.\)=>\(\left[{}\begin{matrix}x=-5\\x=\dfrac{7}{2}\end{matrix}\right.\)