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A = \(\dfrac{3^{100}.\left(-2\right)+3^{101}}{\left(-3\right)^{101}-3^{100}}\)
A = \(\dfrac{3^{100}.\left(-2\right)+3^{100}.3}{\left(-3\right)^{100}.\left(-3\right)-3^{100}}\)
A = \(\dfrac{3^{100}.\left(-2+3\right)}{3^{100}.\left(-3\right)-3^{100}}\)
A = \(\dfrac{3^{100}.1}{3^{100}.\left(-3-1\right)}\)
A = \(\dfrac{3^{100}}{3^{100}}\) . \(\dfrac{1}{-4}\)
A = - \(\dfrac{1}{4}\)
(x - 1) + (x - 2) + (x - 3) + ... + (x - 100) = 50
(x + x + x + ... +x) - (1 + 2 + 3 + ... + 100) = 50
100x - 5050 = 50
100x = 50 + 5050
100x = 5100
x = 5100 : 100 = 51
(x + 1) + (x + 2 ) + (x + 3) + ... + (x - 100) = 50
x - 1 + x - 2 + x - 3 + .... + x - 100 = 50
(x + x + x + ... + x) + (1 - 2 - 3 - ... - 100) = 50
100x + (-2475) = 5750
100x = 5750 - (-2475) = 8225
x = 8225 : 100 = 82,25
\(a)\)\(\left(50-6.x\right).18=2^3.3^2.5\)
\(\Leftrightarrow\)\(\left(50-6.x\right).18=8.9.5\)
\(\Leftrightarrow\)\(\left(50-6.x\right).18=360\)
\(\Leftrightarrow\)\(\left(50-6.x\right)=360\div18\)
\(\Leftrightarrow\)\(50-6.x=20\)
\(\Leftrightarrow\)\(6.x=50-20\)
\(\Leftrightarrow\)\(6.x=30\)
\(\Leftrightarrow\)\(x=5\)
\(b)\)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=7450\)
\(\Leftrightarrow\)\(100x+\left(1+2+3+...+100\right)=7450\)
\(\Leftrightarrow\)\(100x+5050=7450\)
\(\Leftrightarrow\)\(100x=7450-5050\)
\(\Leftrightarrow\)\(100x=2400\)
\(\Leftrightarrow\)\(x=24\)
b.
(x+1)+(x+2)+...+(x+100)=7450
=> 100x + (1+2+3+...+100)=7450
=>100x + (100+1).50=7450
=>100x=2400
=>x=24
(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=50
100x+5050=50
100x=-5000
x=-50
a) 2 + 4 + 6 + ... + 2x = 210
=> 2(1+2+3+4+...+x) = 210
1 + 2 + 3 + .. + x = 210 : 2
1 + 2 + 3 + ... + x = 105
=> Ta có: (x+1)x:2 = 105
(x+1)x = 105.2
(x+1)x = 210
=> (x+1)x = 210 = 15.14
Vậy => x = 14
a) 2+4+6+...+2x=210
<=> {[(2x-2):2+1]:2}.(2x+2) =210
<=> {[2(x-1):2+1]:2}.2(x+1) =210
<=> [(x-1)+1]:2.2(x+1) =210
<=> (x-1+1)(x+1) =210
<=> x(x+1) =210
Vì 14.15=210 nên x=14
b) x + (x - 1) + (x - 2) + ....+ (x - 50) = 255
=> x+x-1+x-2+....+x-50 = 255
=> 51.x-(1+2+3+....+50) = 255
=> 51.x - 1275 = 255
=> 51.x = 1530
=> x = 1530 : 51
=> x = 30
c) (x+1)+(x+2)+....+(x+100)=5750
=> (x+x+...+x)+(1+2+3+...+100)=5750
=> 100x + 5050 = 5750
=> 100x = 700
=> x = 700 : 100
=> x = 7
Gọi BC của 18 và 12 là x
18 = 2 . 32 12 = 22 . 3
BCNN ( 18 , 12) = 22 . 32 = 36
BC ( 18 , 12 ) = B(36) = { 0 , 36 , 72 , 108 , ... }
Mà 50 < x < 100 nên x = 72
\(\left(x-1\right)+\left(x-2\right)+...+\left(x-100\right)=50\)
\(x.100-\left(1+2+...+100\right)=50\)
\(x.100-\left(\left(100+1\right).100:2\right)=50\)
\(x.100-\left(101.100:2\right)=50\)
\(x.100-5050=50\)
\(x.100=50+5050\)
\(x.100=5100\)
\(x=5100:100\)
\(x=51\)