1) (x-3)(x-5) = 0

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=5\end{cases}}\)

(x+7).35 = 2.35

\(\Rightarrow x+7=2\)

\(\Rightarrow x=2-7=-5\)

Vậy x = -5

2) 1.2 + 2.3 + 3.4 + .... + 99.100

Đặt A = 1.2 + 2.3 + .... + 99.100

3A = 1.2.3 + 2.3.4 + 3.4.3 + .... + 99.100.3

3A = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2)+ .... + 99.100.(101-98)

3A = ( 1.2.3 + 2.3.4 + 3.4.5 +.... + 99.100.101 ) - ( 0.1.2 + 1.2.3 + 2.3.4 + ... + 98.99.100 )

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A = 999900

A = 999900 : 3

A = 333300

Vậy A = 333300

1

\(\left(x-3\right)\left(x-5\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}}\)

\(\left(x+7\right).35=2.35\)

\(x+7=2=>x=-5\)

=>y:(1+3+2)x7x5x13=252

=>y:5x7x5x13=252

=>y:5x455=252

=>y:5=252:455

=>y:5=pn tự tính nha

\(y+y:3.7.5+y:2.13=252\\ < =>y+\dfrac{35y}{3}+\dfrac{13y}{2}=252\\ < =>\left(1+\dfrac{35}{3}+\dfrac{13}{2}\right)y=252\\ < =>\dfrac{115}{6}y=252\\ =>y=\dfrac{252}{\dfrac{115}{6}}=\dfrac{1512}{115}\)

Có : 7/2^2.35 = 7/2^2.5.7 = 1/2^2.5

9/2^2.3^2.10 = 3^2/2^2.3^2/10 = 1/2^2.10

Vì 2^2.5 < 2^2.10 

=> 1/2^2.5 > 1/2^2.10

=> 7/2^2.35 > 9/2^2.3^2.10

Tk mk nha

tinh hop li

Ta có

kết quả là:

x = 0

x = -5

x = 21

nha bn

45 . ( 2.x - 4 ) . 13 = 0

45 . 13 . ( 2.x - 4 ) = 0

585 . ( 2.x - 4 ) = 0

( 2.x - 4 ) = 0 : 585

 2.x - 4  = 0

2.x = 0 + 4

2.x = 4

x = 4 : 2

x = 2

( x + 7 ) . 35 = 2.35

 x + 7  = ( 2 . 35 ) : 35

x + 7 = 35

x = 35 - 7

x = 28

43 . ( x - 19 ) = 86

x - 19 = 86 : 43

x - 19 = 2

x = 2 + 19

x = 21

\(x-\dfrac{12}{8\cdot11}-\dfrac{12}{11\cdot14}-\dfrac{12}{14\cdot17}-...-\dfrac{12}{32\cdot35}=\dfrac{43}{70}\) (phải là `32*35` chứ nhỉ?)

\(x-\left(\dfrac{12}{8\cdot11}+\dfrac{12}{11\cdot14}+\dfrac{12}{14\cdot17}+...+\dfrac{12}{32\cdot35}\right)=\dfrac{43}{70}\)

\(x-4\left(\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{3}{14\cdot17}+...+\dfrac{3}{32\cdot35}\right)=\dfrac{43}{70}\)

\(x-4\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+...+\dfrac{1}{32}-\dfrac{1}{35}\right)=\dfrac{43}{70}\)

\(x-4\left(\dfrac{1}{8}-\dfrac{1}{35}\right)=\dfrac{43}{70}\\ x-4\cdot\dfrac{27}{280}=\dfrac{43}{70}\)

\(x-\dfrac{27}{70}=\dfrac{43}{70}\\ x=\dfrac{43}{70}+\dfrac{27}{70}\\ x=\dfrac{70}{70}=1\)

cái -12/2.35 thành  -12/32.35 nha

\(A=\frac{4^5.13+32^2.65}{4^4.104}=\frac{2^{10}.13+2^{10}.13.5}{2^8.2^3.13}=\frac{2^{10}.13.\left(1+5\right)}{2^{11}.13}=\frac{6}{2}=3\)

Vậy A = 3

2) \(x\in UCLN\left(35;130\right)=\left\{5\right\}\)

3) \(B=2^2+2^2+2^3+...+2^{20}=2^3+2^3+...+2^{20}=2^{21}\)