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a: \(\left(x-2\right)^2-\left(2x+3\right)^2=0\)
=>(x-2-2x-3)(x-2+2x+3)=0
=>(-x-5)(3x+1)=0
=>(x+5)(3x+1)=0
=>\(\left[\begin{array}{l}x+5=0\\ 3x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-5\\ x=-\frac13\end{array}\right.\)
b: \(9\left(2x+1\right)^2-4\left(x+1\right)^2=0\)
=>\(\left\lbrack3\left(2x+1\right)\right\rbrack^2-\left\lbrack2\left(x+1\right)\right\rbrack^2=0\)
=>\(\left(6x+3\right)^2-\left(2x+2\right)^2=0\)
=>(6x+3+2x+2)(6x+3-2x-2)=0
=>(8x+5)(4x+1)=0
=>\(\left[\begin{array}{l}8x+5=0\\ 4x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac58\\ x=-\frac14\end{array}\right.\)
c: \(x^3-6x^2+9x=0\)
=>\(x\left(x^2-6x+9\right)=0\)
=>\(x\left(x-3\right)^2=0\)
=>\(\left[\begin{array}{l}x=0\\ \left(x-3\right)^2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=3\end{array}\right.\)
d: \(x^2\left(x+1\right)-x\left(x+1\right)+x\left(x-1\right)=0\)
=>\(\left(x+1\right)\left(x^2-x\right)+x\left(x-1\right)=0\)
=>x(x+1)(x-1)+x(x-1)=0
=>x(x-1)(x+1+1)=0
=>x(x-1)(x+2)=0
=>\(\left[\begin{array}{l}x=0\\ x-1=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\\ x=-2\end{array}\right.\)
e: \(\left(x-2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
=>(x-2)(x-2-x-2)=0
=>-4(x-2)=0
=>x-2=0
=>x=2
g: \(x^4-2x^2+1=0\)
=>\(\left(x^2-1\right)^2=0\)
=>\(x^2-1=0\)
=>\(x^2=1\)
=>\(\left[\begin{array}{l}x=1\\ x=-1\end{array}\right.\)
h: \(4x^2+y^2-20x-2y+26=0\)
=>\(4x^2-20x+25+y^2-2y+1=0\)
=>\(\left(2x-5\right)^2+\left(y-1\right)^2=0\)
=>\(\begin{cases}2x-5=0\\ y-1=0\end{cases}\Rightarrow\begin{cases}x=\frac52\\ y=1\end{cases}\)
i: \(x^2-2x+5+y^2-4y=0\)
=>\(x^2-2x+1+y^2-4y+4=0\)
=>\(\left(x-1\right)^2+\left(y-2\right)^2=0\)
=>\(\begin{cases}x-1=0\\ y-2=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=2\end{cases}\)
a) x = 1; x = - 1 3 b) x = 2.
c) x = 3; x = -2. d) x = -3; x = 0; x = 2.
a)\(\left(x-2\right)^2-\left(2x+3\right)^2=0\Rightarrow\left(x-2+2x+3\right)\left(x-2-2x-3\right)=0\)
\(\Rightarrow\left(3x+1\right)\left(-x-5\right)=0\Rightarrow\left[{}\begin{matrix}3x+1=0\\-x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=-5\end{matrix}\right.\)
b)\(9\left(2x+1\right)^2-4\left(x+1\right)^2=0\Rightarrow\left[3\left(2x+1\right)+2\left(x+1\right)\right]\left[3\left(2x+1\right)-2\left(x+1\right)\right]=0\)
\(\Rightarrow\left[8x+5\right]\left[4x+1\right]=0\Rightarrow\left[{}\begin{matrix}8x+5=0\\4x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{8}\\x=\dfrac{1}{4}\end{matrix}\right.\)
c)\(x^3-6x^2+9x=0\Rightarrow x\left(x^2-6x+9\right)=0\Rightarrow x\left(x-3\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
d) \(x^2\left(x+1\right)-x\left(x+1\right)+x\left(x-1\right)=0\)
\(\Rightarrow x\left(x+1\right)\left(x^2-1\right)+x\left(x-1\right)=0\)
\(\Rightarrow x\left(x+1\right)\left(x-1\right)\left(x+1\right)+x\left(x-1\right)=0\)
\(\Rightarrow x\left(x-1\right)\left[\left(x+1\right)\left(x+1\right)+1\right]=0\)
\(\Rightarrow x\left(x-1\right)\left[\left(x+1\right)^2+1\right]=0\)
Do \(\left(x+1\right)^2+1>0\)
\(\Rightarrow x\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\\x=1\end{matrix}\right.\)
d: \(\Leftrightarrow\left(x+3\right)\left(x^2-4x+5\right)=0\)
\(\Leftrightarrow x+3=0\)
hay x=-3
Câu 2:
a: \(\left(x-1\right)\left(x+1\right)-x\left(x+3\right)+7=0\)
=>\(x^2-1-x^2-3x+7=0\)
=>-3x+6=0
=>-3x=-6
=>\(x=\dfrac{-6}{-3}=2\)
b: \(2x^3-22x^2+36x=0\)
=>\(2x\left(x^2-11x+18\right)=0\)
=>\(x\left(x^2-11x+18\right)=0\)
=>\(x\left(x^2-2x-9x+18\right)=0\)
=>\(x\left[x\left(x-2\right)-9\left(x-2\right)\right]=0\)
=>\(x\left(x-2\right)\left(x-9\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-2=0\\x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=9\end{matrix}\right.\)
Câu 4:
1: Diện tích cỏ cần thay là:
\(105\cdot68=7140\left(m^2\right)\)
Số tiền BQL sân cần trả là:
\(7140\cdot120000=856800000\left(đồng\right)\)
2:
a: Xét tứ giác ABDC có
M là trung điểm chung của AD và BC
=>ABDC là hình bình hành
Hình bình hành ABDC có \(\widehat{BAC}=90^0\)
nên ABDC là hình chữ nhật
b: Xét ΔADE có
H,M lần lượt là trung điểm của AE,AD
=>HM là đường trung bình của ΔADE
=>HM//DE
=>BC//DE
=>\(\widehat{EDB}=\widehat{DBM}\)(hai góc so le trong)(1)
Ta có: ABDC là hình chữ nhật
=>AD=BC
mà \(MD=\dfrac{AD}{2};MB=\dfrac{BC}{2}\)
nên MD=MB
=>ΔMBD cân tại M
=>\(\widehat{MDB}=\widehat{MBD}\left(2\right)\)
Từ (1) và (2) suy ra \(\widehat{MDB}=\widehat{EDB}\)
=>\(\widehat{ADB}=\widehat{EDB}\)
=>DB là phân giác của góc ADE
a,\(x^3-\dfrac{1}{9}=0\)
\(\Rightarrow x^3-\left(\dfrac{1}{3}\right)^3=0\)
\(\Rightarrow\left(x-\dfrac{1}{3}\right)\left(x^2+\dfrac{1}{3}x+\dfrac{1}{9}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=0\\x^2+\dfrac{1}{3}x+\dfrac{1}{9}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x^2+\dfrac{1}{3}x=-\dfrac{1}{9}\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{1}{3}\)