Tính nhanh các phép chia sau: 625 x 4 - 1 : ( 5 x + 1 ) ( 5 x - 1 )
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1x2x3x4x5x6=720. 720 chia hết cho 5, cụ thể chia 5 dư 1x2x3x4x6=144. (P+1) chia 5 cũng thương là 144 và dư 1
Bài 1:
b: \(=\dfrac{x+3-4-x}{x-2}=\dfrac{-1}{x-2}\)
Bài 2:
a: \(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)
\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
d: \(=\dfrac{3}{2x^2y}+\dfrac{5}{xy^2}+\dfrac{x}{y^3}\)
\(=\dfrac{3y^2+10xy+2x^3}{2x^2y^3}\)
e: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2x^2-4xy}{\left(x+2y\right)\cdot\left(x-2y\right)}=\dfrac{2x}{x+2y}\)
a) ta thấy 1/2x3 + 1/3x4 + 1/4 x 5 + ...... + 1/a x ( a + 1 ) = 1/2 - 1/3 + 1/3 -1/4 +............+ 1/a - 1/a+1 = 49/100
1/2 - 1/a+1= 49/100
1/a+1=1/2 - 49/100
1/a + 1= 1/100
a + 1= 100
a= 100 - 1
a= 99
b) ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16) x ..... x (1 - 1/625)
= 3/4 x 8/9 x 15/16 x...........x 575/576x 624/625 = 1x3/1x4 x 2x4/ 3x3 x 3x5/4 x 4x.................x 23x 25/ 24 x 24 x 24x26/ 25x25
= ( 1/1 x 2/3 x 3/4 x 4/5 x .................x 23/24 x 24/25= 1x2x3x4x..............23x24/ 1 x 3 x 4 x5x............24x25=2/25)
( 3/5 x 4/3 x 5/4 x 6/5x.............x 25/24 x 26/25= 3 x 4 x 5x 6 x ............x 25x 26/ 5 x 3 x 4 x 5x............x 24 x 25= 26/5)
2/25 x 26/5= 52/30= 26/25
\(\begin{array}{l}a)3{x^7}:\dfrac{1}{2}{x^4} = (3:\dfrac{1}{2}).({x^7}:{x^4}) = 6{x^3}\\b)( - 2x):x = [( - 2):1].(x:x) = - 2\\c)0,25{x^5}:( - 5{x^2}) = [0,25:( - 5)].({x^5}:{x^2}) = - 0,05.{x^3}\end{array}\)
2.
a) (2x + 1)3 = 125
(2x + 1)3 = 53
2x + 1 = 5
2x = 5 - 1
2x = 4
x = 4:2
x = 2
Vậy x = 2
b) 5x+1 = 54
x + 1 = 4
x = 4 - 1
x = 3
Vây x = 3
a) \(A=1.2+2.3+3.4+...+98.99+99.100\)
\(3A=1.2.3+2.3.4+3.4.3+...+99.100.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)....99.100.\left(101-98\right)\)
\(3A=\left(1.2.3+2.3.4+3.4.5+...+99.100.101\right)-\left(0.1.2+1.2.3+2.3.4+...+98.99.100\right)\)
\(3A=99.100.101-0.1.2\)
\(3A=999900-0\)
\(3A=999900\)
\(A=999900:3\)
\(\Rightarrow A=333300\)
2:
a: =>-2x=10
=>x=-5
b: =>(x-3)(2x+5)=0
=>x=3 hoặc x=-5/2