`5x+4x^2=0`

`<=>x(5+4x)=0`

TH1: x=0

TH2: `5+4x=0`

`<=>4x=-5`

`<=>x=-5/4`

Vậy: ... 

\(A=2^2+2^4+2^6+...+2^{200}\\ 2^2A=2^4+2^6+...+2^{202}\\ 4A-A=\left(2^4+2^6+2^8+...+2^{202}\right)-\left(2^2+2^4+2^6+...+2^{200}\right)\\ 3A=2^{202}-2^2\) 

\(=>3A+4=2^{202}-2^2+4=2^{202}-4+4=2^{202}\) 

\(=>2^{202}=4^n\\ =>2^{202}=\left(2^2\right)^n\\ =>2^{202}=2^{2n}\\ =>2n=202\\ =>n=101\)

ABCD là hình vuông

=>AB//CD

mà C\(\in\)DE

nên AB//DE

Ta có: DEFG là hình chữ nhật

=>DE//FG

mà AB//DE

nên AB//FG

a: \(\left(x+4\right)\left(x^2-4x+16\right)\)

\(=\left(x+4\right)\left(x^2-x\cdot4+4^2\right)\)

\(=x^3+4^3=x^3+64\)

b: \(\left(x-5\right)\left(x^2+5x+25\right)\)

\(=\left(x-5\right)\left(x^2+x\cdot5+5^2\right)\)

\(=x^3-5^3=x^3-125\)

c: \(\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\)

\(=x^6+\dfrac{1}{3}x^4+\dfrac{1}{9}x^2-\dfrac{1}{3}x^4-\dfrac{1}{9}x^2-\dfrac{1}{27}\)

\(=x^6-\dfrac{1}{27}\)

d: \(\left(4x^2+2xy+y^2\right)\left(2x-y\right)\)

\(=8x^3-4x^2y+4x^2y-2xy^2+2xy^2-y^3\)

\(=8x^3-y^3\)

\(a.\left(x+4\right)\left(x^2-4x+16\right)\\ =\left(x+4\right)\left(x^2-4\cdot x+4^2\right)\\ =x^3+4^3\\ =x^3+64\\ b.\left(x-5\right)\left(x^2+5x+25\right)\\ =\left(x-5\right)\left(x^2+5\cdot x+5^2\right)\\ =x^3-5^3\\ =x^3-125\\ c.\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\\ =\left(x^2-\dfrac{1}{3}\right)\left[\left(x^2\right)^2+\dfrac{1}{3}\cdot x^2+\left(\dfrac{1}{3}\right)^2\right]\\ =\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3\\ =x^6-\dfrac{1}{27}\\ d.\left(4x^2+2xy+y^2\right)\left(2x-y\right)\\ =\left(2x-y\right)\left[\left(2x\right)^2+2x\cdot y+y^2\right]\\=\left(2x\right)^3-y^3\\ =8x^3-y^3\)

\(42\cdot136+272\cdot15+28\cdot68\cdot2\)

\(=42\cdot136+30\cdot136+28\cdot136\)

\(=136\left(42+30+28\right)\)

\(=136\cdot100=13600\)

42 x 136 + 272 x 15 + 28 x 68 x 2

= 21 x (2 x 136) + 272 x 15 + (68 x 4) x 7 x 2 

= 21 x 272 + 272 x 15 + 272 x 14

= 272 x (21 + 15 + 14)

= 272 x 50

= 13600

62,58>62,08

9,001<9,1

62,58>62,08

9,001<9,1

a: \(\left(x-2\right)\left(3x-1\right)\left(x^2-4x+1\right)\)

\(=\left(3x^2-x-6x+2\right)\left(x^2-4x+1\right)\)

\(=\left(3x^2-7x+2\right)\left(x^2-4x+1\right)\)

\(=3x^4-12x^3+3x^2-7x^3+28x^2-7x+2x^2-8x+2\)

\(=3x^4-19x^3+33x^2-15x+2\)

b: \(x\left(3-4x\right)\left(2x^2-3x\right)\)

\(=\left(-4x^2+3x\right)\left(2x^2-3x\right)\)

\(=-8x^4+12x^3+6x^3-9x^2\)

\(=-8x^4+18x^3-9x^2\)

a) 

\(\left(x-2\right)\left(3x-1\right)\left(x^2-4x+1\right)\\ =\left(3x^2-6x-x+2\right)\left(x^2-4x+1\right)\\ =\left(3x^2-7x+2\right)\left(x^2-4x+1\right)\\ =3x^4-12x^3+3x^2-7x^3+28x^2-7x-8x+2\\ =3x^4-19x^3+31x^2-15x+2\) 

b) 

\(x\left(3-4x\right)\left(2x^2-3x\right)\\ =\left(3x-4x^2\right)\left(2x^2-3x\right)\\ =6x^3-9x^2-8x^4+12x^3\\ =-8x^4+18x^3-9x^2\)

\(x^7+x^2+1\)

\(=x^7+x^6+x^5-x^6-x^5-x^4+x^4+x^3+x^2-x^3-x^2-x+x^2+x+1\)

\(=x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)

Bài 1: Chiều dài mảnh đất là 132:4=33(m)

Chu vi miếng đất là \(\left(33+4\right)\times2=74\left(m\right)\)

Bài 1: 

Chiều dài mảnh đất là:

\(132:4=33\left(m\right)\)

Chu vi mảnh đất là:

\(\left(33+4\right)\times2=74\left(m\right)\)

Đáp số: 72 m

Bài 2:

Đổi \(14m5dm=145dm;2m=20dm\)

Chu vi mảnh vườn là:

\(145\times4=580\left(dm\right)\)

Độ dài hàng rào là:

\(580-2=578\left(dm\right)\)

Đáp số: 578 dm
 

a) 

\(32< 2^x< 128\\ =>2^5< 2^x< 2^7\\ =>5< x< 7\\ =>x=6\)

b) 

\(2\cdot16\ge2^x>4\\ =>2\cdot2^4\ge2^x>2^2\\ =>2^5\ge2^x>2^2\\ =>5\ge x>2\\ =>x\in\left\{3;4;5\right\}\)

c) 

\(9\cdot27\le3^x\le243\\ =>3^2\cdot3^3\le3^x\le3^5\\ =>3^5\le3^x\le3^5\\ =>5\le x\le5\\ =>x=5\)

d) 

\(x^{2019}=x\\ =>x^{2019}-x=0\\ =>x\left(x^{2018}-1\right)=0\)

TH1: x = 0

TH2: `x^2018-1=0`

`=>x^2018=1`

`=>x^2018=1^2018`

`=>x=1` hoặc `x=-1`

a: \(32< 2^x< 128\)

=>\(2^5< 2^x< 2^7\)

=>5<x<7

mà x là số tự nhiên

nên x=6

b: \(2\cdot16>=2^x>4\)

=>\(2^5>=2^x>2^2\)

=>2<x<=5

mà x là số tự nhiên

nên \(x\in\left\{3;4;5\right\}\)

c: \(9\cdot27< =3^x< =243\)

=>\(243< =3^x< =243\)

=>\(3^x=243=3^5\)

=>x=5

d: \(x^{2019}=x\)

=>\(x\left(x^{2018}-1\right)=0\)

=>\(\left[{}\begin{matrix}x=0\\x^{2018}-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^{2018}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

e: \(2^{x+1}+4\cdot2^x=3\cdot2^7\)

=>\(2^x\cdot2+4\cdot2^x=6\cdot2^6\)

=>\(6\cdot2^x=6\cdot2^6\)

=>x=6

f: \(2^{2x}+2^{2x+3}=3^2\cdot8^4\)

=>\(2^{2x}+2^{2x}\cdot8=9\cdot8^4\)

=>\(9\cdot2^{2x}=9\cdot2^{12}\)

=>2x=12

=>x=6

g: \(27^{x+1}=9^{x+5}\)

=>\(3^{3\left(x+1\right)}=3^{2\left(x+5\right)}\)

=>3(x+1)=2(x+5)

=>3x+3=2x+10

=>3x-2x=10-3

=>x=7

h: \(3^{x+2}+5\cdot3^{x+1}=648\)

=>\(3^x\cdot9+5\cdot3^x\cdot3=648\)

=>\(3^x\cdot24=648\)

=>\(3^x=\dfrac{648}{24}=27=3^3\)

=>x=3