Bài 1:

B = 1+2-3-4 + 5 + 6-7-8 + 9+10-11-12+...+110-111-112+113+114

B = 1 + (-5) + 5 + 9 + (-13)+...+ (-113) + 113 + 114

B = 1 + 114

B = 115

Bài 2:

697 : [(15x+364) : x ] = 17

(15x+364) . 1/x = 697 : 17

(15x+364) . 1/x = 41

15x. 1/x + 364.1/x = 41

15 + 364/x = 41

364/ x = 41-15

364/x = 26

x = 364 : 26

x = 14

Ta sẽ nhóm 4 số với nhau

B=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+...+(109+110-111-112)+113+114

B=-4+(-4)+(-4)+...+(-4)+113+114 (Có 28 thừa số -4)

B=-4*28+113+114

Giải tiếp bên dưới hồi nãy ấn nhầm:

B=-112+113+114

B=115

Bài 2

697:[(15X+364):X]=17

(15X+364)x1/X=697:17

(15X+364)x1/X=41

15Xx1/X+364x1/X=41

15+364/X=41

364/X=41-15

364/X=26

X=364/26

X=14

1,

=66

2,

=28

3,

=2016+450-2016

=450

4, 

=360-360+111

=111

5,

=1972-638-972

=1972-972-638

=362

1) = 27 + 37 + 2

= 64 + 2 = 66

2) = 6 + 26 - 4 = 32 - 4 = 28

3) = (2016-2016)+450 = 450

4) =(364-364)+111 = 111

5) = (1972-972)-638 = 1000 - 638 = 362

1. 5 + 22 + 37 + 2

= 27 + 39

= 66

2. 12 - 6 + 26 - 4

= 6 + 22

= 28

3. (2016 + 450) - 2016

= 2016 + 450 - 2016

= 2016 - 2016 + 450

= 450

4. 364 - (364 - 111)

= 364 - 364 + 111

= 0 + 111

= 111

5. 1972 - (638 + 972)

= 1972 - 638 - 972

= 1972 - 972 - 638

= 1000 - 638 

= 362

a: B=(1+2-3-4)+(5+6-7-8)+...+(109+110-111-112)+227

=(-4)+(-4)+...+(-4)+227

=-112+227=115

b: =>(15x+364):x=41

=>15x+364=41x

=>-26x=-364

=>x=14

a, 364 - ( 364 - 111 )

= ( 364 - 364 ) + 111

= 0 + 111

= 111

b, 249 - ( 75 - 51 ) 

= ( 249 + 51 ) - 75

= 300 - 75

= 225

1, Tính nhanh 

a,364-(364-111)

b,249-(75-51)

c,100+98+96+..+2-97-95-...-1

1) 

a) \(364-\left(364-111\right)\)

\(=364-364+111\)

\(=\left(364-364\right)+111\)

\(=0+111=111\)

b) \(249-\left(75-51\right)\)

\(=249-75+51\)

\(=\left(249+51\right)-75\)

\(=300-75=225\)

364-(364-111)=364-364+111=111

249-(75-51)=(249+51)-75=300-75=225

364-(364-111)=111

249-(75-51)=225

C1: * 364 - (364 - 111)

= 364 - 364 + 111

= 111

       * 249 - (75 - 51)

= 249 - 75 + 51

= (249 + 51) - 75

= 300 - 75

= 225

C2: * 364 - (364 - 111)

= 364 - 253

= 111

       * 249 - (75 - 51)

= 249 - 24

= 225

Giải :

( 1435 + 213 ) – 13 = 1435 + ( 213 – 13 ) = 1435 + 200 = 1635

1972 – ( 364 + 972 ) = 1972 – 972 – 368 = 1000 – 368 = 632

      c.    364 – ( 364 – 111 ) = 364 – 364 + 111 = 111

             249 – ( 75-51 ) = ( 249 + 51 ) – 75 = 300 – 75 = 225

\(\left|x\right|=1+2+3+...+2010\)

\(\left|x\right|=\frac{\left(2010+1\right).2010}{2}\)

\(\left|x\right|=2011.1005\)

\(\left|x\right|=2021055\)

\(x=\pm2021055\)

\(2^x=2+4+6+...+2010\)

\(2^x=\frac{\left(2010+2\right).1005}{2}\)

\(2^x=1006.1005\)

\(x=\frac{log\left(1011030\right)}{log\left(2\right)}\)(Nguồn: wolframalpha)

\(697\div15a+\frac{364}{a}=17\)

\(\frac{697}{15a}+\frac{5460}{15a}=17\)

\(6157=17.15a\)

\(6197=255a\)

\(a=\frac{6197}{255}\)