a, 333...333 (100 chữ số 3).333...33(100 chữ số 3)

= 333...333²(100 chữ số 3)

b, A = (100 - 1).(100 - 2)....(100- n)

    Vì tích trên có 100 thừa số nên n = 100

Vậy A = (100 - 1).(100 -2)...(100 - 100)

       A = (100 - 1).(100 - 2)...0

      A = 0

Bài 2:

a, 25.\(x\) - 3⁴ = 2².5 + 2.(7\(x\) + 4) + 216⁰

   25\(x\) - 81 = 20 + 14\(x\) + 8 + 1

   25\(x\)  - 14\(x\) = 20 + 8 + 1 + 81

   11\(x\)          = 110

       \(x\)         = \(\dfrac{110}{11}\)

b, 9\(^{4x}\) : 81\(^x\) = 27⁸

    \(\left(3^2\right)^{4x}\) : \(\left(3^4\right)^x\) = (3³)⁸

       \(3^{8x}\)   : \(3^{4x}\)  = 3²⁴

       \(3^{4x}\)            = 3²⁴

       4\(x\)            = 24

         \(x\)            = 24 : 4

         \(x\)            = 6

1.

a.

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)

b.

Tích có 100 thừa số 

=> n = 100

\(\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times\left(100-100\right)\)

\(=\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times0\)

\(=0\)

2.

a.

\(135\times789789-789\times135135=1001\times\left(135\times789-789\times135\right)=1001\times0=0\)

b.

\(\left(28\times9696-96\times2828\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)

\(=\left[101\times\left(28\times96-96\times28\right)\right]\div\left(1\times2\times3\times...\times2015\times2016\right)\)

\(=\left(101\times0\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)

\(=0\div\left(1\times2\times3\times...\times2015\times2016\right)\)

\(=0\)

3.

a.

\(\left[\left(x+32\right)-17\right]\times2=42\)

\(\left(x+32\right)-17=\frac{42}{2}\)

\(\left(x+32\right)-17=21\)

\(x+32=21+17\)

\(x+32=38\)

\(x=38-32\)

\(x=6\)

b.

\(125+\left(145-x\right)=175\)

\(145-x=175-125\)

\(145-x=50\)

\(x=145-50\)

\(x=95\)

A=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6

A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

A=1-1/6

A=5/6

Vậy: A=5/6

B=(100-1).(100-2).(100-3). ... .(100-n)

B=99.98.97. ... .0

B=0

Vậy B=0

              Chắc Vậy

Bài 4 : Tính nhanh :
a, 15. 64 + 25. 100 + 36. 15 + 60. 100

= (15 . 64 + 36. 15) + (25. 100 + 60. 100)

= 15.(64 + 36) + 100.(25 + 60)

= 15. 100 + 100. 85

= 100.(15 + 85)

= 100. 100

= 10000
b, 47² + 48² - 25 + 94. 48

= 47² + 2.47. 48 + 48² - 25

= (47 + 48)² - 5²

= (47 + 48 - 5)(47 + 48 + 5)

= (48 + 22)(48 + 52)

= 90. 100

= 9000
c, 9³ - 9². ( -1) - 9. 11 + ( -1). 11

= 9³ + 9² + 11(- 9 - 1)

= 9².(9 + 1) + 11. (-10)

= 81. 10 - 110

= 810 - 110

= 700
d,2016. 2018 - 2017²

= (2017 - 1)(2017 + 1) - 2017²

= 2017² - 1 - 2017²

= -1

#Học tốt!

Bài 1: Tìm x

a) x . (x + 3) = 0

=> \(\orbr{\begin{cases}x=0\\x+3=0\end{cases}}\)

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

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

b) (x -1) (x² - 1) = 0

=> \(\orbr{\begin{cases}x-1=0\\x^2-1=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=0+1\\x^2=0+1\left(bỏ\right)\end{cases}}\)

=> x = 1

Bài 2: Tìm x, biết

a) -12(x - 5) + 7(3 - x) = 5

-12x - (-12 . 5) + 7 . 3 - 7x = 5

-12x + 60 + 21 - 7x = 5

-12x - 7x = 5 - 21 - 60

-19x = -76

x = -76 : (-19)

x = 4

Thanks pạn nha

B=(xyz)+(xyz)^2+(xyz)^3+...+(xyz)^100

=(-1)+1+(-1)+1+...+(-1)+1

=0

B