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a)\(=\frac{45\cdot\left(15+1\right)-17}{45\cdot15+28}\)
\(=\frac{45\cdot15+45-17}{45\cdot15+28}\)
\(=\frac{45\cdot15+28}{45\cdot15+28}\)
=1
b)=>(x+1)[(x-1):3+1]:2=330
=>(x+1)[(x-1):3+1]=660
=>(x+1)[(x-1):3+1]=44.15
=>x+1=44
=>x=43
1) \(\frac{3^{10}+6^2}{5\cdot3^8+20}=\frac{3^{10}+3^2\cdot2^2}{5\cdot3^8+5\cdot2^2}=\frac{3^2\left(3^8+2^2\right)}{5\left(3^8+2^2\right)}=\frac{9}{5}\)
2) \(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{28^{15}\cdot3^{17}}{28^{16}\cdot3^{16}}=\frac{3}{28}\)
a ) 5 x 216 x 25 x 4 = 1080 x 100 = 108000
b ) 37 x 16 x 25 x 4 = 592 x 100 = 59200
c ) 36 x ( 28 + 82 ) + 64 x ( 69 + 41 ) = 36 x 110 + 64 x 110 = ( 36 + 64 ) x 110 = 100 x 110 = 11000
d ) 42 x ( 53 + 36 + 11 ) = 42 x 100 = 4200
e) 37 x 45 + 56 x 37 - 37 x 1 = 37 x ( 45 + 56 - 1 ) = 37 x 100 = 3700
h) 17 x 1 + 17 x 81 + 18 x 17 = 17 x ( 1 + 81 + 18 ) = 17 x 100 = 1700
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a) 5 x 25 x 216 x 4
= ( 5 x 216 ) x ( 25 x 4 )
= 1080 x 100
= 108000
b) 4 x 37 x 25 x 16
= ( 4 x 25 ) x ( 37 x 16 )
= 100 x 592
= 59200
12/15 = 4/5 15/10 = 3/2
14/21 = 2/3 70/20 = 7/2
18/12 = 3/2 55/66 = 5/6
( 4/5 - 2/3 - 3/2 ) : ( 3/2 - 7/2 - 5/6 ) = -41/30 : -17/6
= 41/85
\(A=\dfrac{17^{100}+17^{96}+17^{92}+....+17^4+1}{17^{102}+17^{100}+17^{98}+....+17^2+1}\)
Gọi \(17^{100}+17^{96}+17^{92}+....+17^4+1\) là B
\(B=17^{100}+17^{96}+17^{92}+....+17^4+1\\ 17^4\cdot B=17^{104}+17^{100}+17^{96}+......+17^8+17^4\\ 17^4\cdot B-B=\left(17^{104}+17^{100}+17^{96}+......+17^8+17^4\right)-\left(17^{100}+17^{96}+17^{92}+....+17^4+1\right)\\ B\cdot\left(17^4-1\right)=17^{104}-1\\ B=\dfrac{17^{104}-1}{17^4-1}\)
Gọi \(17^{102}+17^{100}+17^{98}+....+17^2+1\) là C
\(C=17^{102}+17^{100}+17^{98}+....+17^2+1\\ C\cdot17^2=17^{104}+17^{102}+17^{100}+17^{98}+....+17^2\\ C\cdot17^2-C=\left(17^{104}+17^{102}+17^{100}+17^{98}+....+17^2\right)-\left(17^{102}+17^{100}+17^{98}+....+17^2+1\right)\\ C\cdot\left(17^2-1\right)=17^{104}-1\\ C=\dfrac{17^{104}-1}{17^2-1}\)
=>
\(A=B:C\\ A=\dfrac{17^{104}-1}{17^4-1}:\dfrac{17^{104}-1}{17^2-1}\\ A=\dfrac{17^2-1}{17^4-1}\)
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