(1-1/16)x(1-1/25)x(1-1/49)x...x(1-1/100)
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có 2014 là số chẵn => 2014^x là số chẵn
có 4 là số chẵn => 4y là số chẵn
=> 2014^x+4y là số chẵn mà 2013 là số lẻ
=> không có giá trị của x,y dể 2014^y+4y=2013
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 3/7 + 4/9 + 4/7 + 5/9
= ( 3/7 + 4/7 ) + ( 4/9 + 5/9 )
= 7/7 + 9/9
= 1 + 1
= 2
b)1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45
= 1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5
= ( 1/5 + 9/5 ) + ( 2/5 + 8/5 ) + (7/5 + 3/5 ) + ( 4/5 + 6/5 ) + 5/5
= 2 + 2 + 2 + 2 + 1
= 2 x 4 + 1
= 8 +1
= 9
c) 1/8 + 1/12 + 3/8 + 5/12
= ( 1/8 + 3/8 ) + ( 1/12 + 5/12)
= 4/8 + 6/12
= 1/2 + 1/2
= 2/4 = 1/2
mỏi tay rồi
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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
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a) Ta có: \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)
\(=\left(x^2+1\right)^2-2\cdot\left(x^2+1\right)\cdot3+3^2\)
\(=\left(x^2+1-3\right)^2\)
\(=\left(x^2-2\right)^2\)
b) Ta có: \(16\left(x+1\right)^2-25\left(2x+3\right)^2\)
\(=\left[4\left(x+1\right)\right]^2-\left[5\left(2x+3\right)\right]^2\)
\(=\left(4x+4\right)^2-\left(10x+15\right)^2\)
\(=\left(4x+4-10x-15\right)\left(4x+4+10x+15\right)\)
\(=\left(-6x-11\right)\left(14x+19\right)\)
c) Ta có: \(x^{16}-1\)
\(=\left(x^8+1\right)\left(x^8-1\right)\)
\(=\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
d) Ta có: \(49\left(x+y\right)^2-36\left(2x+3y\right)^2\)
\(=\left[7\left(x+y\right)\right]^2-\left[6\left(2x+3y\right)\right]^2\)
\(=\left(7x+7y\right)^2-\left(12x+18y\right)^2\)
\(=\left(7x+7y-12x-18y\right)\left(7x+7y+12x+18y\right)\)
\(=\left(-5x-11y\right)\left(19x+25y\right)\)
e) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2\cdot\left(x+y\right)\cdot1+1^2\)
\(=\left(x+y-1\right)^2\)
f) Ta có: \(x^6-8\)
\(=\left(x^2\right)^3-2^3\)
\(=\left(x^2-2\right)\left(x^4+2x^2+4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
m) \(\dfrac{1}{4}x^2-4x^2=\left(\dfrac{1}{2}x-2x\right)\left(\dfrac{1}{2}x+2x\right)\)
n) \(\dfrac{4}{49}-4x^2=\left(\dfrac{2}{7}-2x\right)\left(\dfrac{2}{7}+2x\right)\)
o) \(\left(x-3\right)\left(x+3\right)=x^2-9\)
=15/16x24/25x...x99/100
=3x5/4x4 x 4x6/5x5 x...x 9x11/10x10
=(3x4x...x9) x (5x6x...x11)/ (4x5x...x10)x(4x5x....x10)
=3x11/10x4
=33/40
đúng ko bạn?