\(1-x=\frac{29}{12}+\frac{32}{8}\)

\(\Rightarrow1-x=\frac{77}{12}\)

\(\Rightarrow x=1-\frac{77}{12}=\frac{-65}{12}\)

\(\frac{31}{8}.x-\frac{11}{4}=\frac{42}{12}.\frac{10}{8}-\frac{1}{3}\)

\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{35}{8}-\frac{1}{3}\)

\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{97}{24}\)

\(\Rightarrow\frac{31}{8}.x=\frac{97}{24}+\frac{11}{4}=\frac{163}{24}\)

\(\Rightarrow x=\frac{163}{24}:\frac{31}{8}=\frac{163}{93}\)

a,  2 3 x + 5 2 x = 2 5 2 + 2 3 - 33

8x+25x = 33

33x = 33

x = 1

b,  260 : x + 4 = 5 2 3 + 5 - 3 3 2 + 2 2

260:(x+4) = 5.13–3.13

x+4 = 260:26

x+4 = 10

x = 6

c,  720 : [ 41 - 2 x - 5 ] = 2 3 . 5

41–(2x–5) = 720:40

2x–5 = 41–18

2x = 28

x = 14

d,  3 2 - 2 x - 12 + 35 = 5 2 + 279 : 3 2

7(x–12)+35 = 56

7(x–12) = 21

x–12 = 3

x = 15

1, đúng òi

2, đúng òi

3, sai òi

4, đúng òi

5, s

x = -4 hoặc x = 23 

Bài 1 :

A = 1² + 2² + 3² +....+n² 

A = 1² + 2.(1+1) + 3.(2 +1) + 4.( 3 +1) +.....+n(n-1 + 1)

A = 1 + 1.2 + 2 + 2.3 + 3 + 3.4 + 4 +.....+ n.(n-1) + n

A = ( 1 + 2 + 3 + 4 +....+n) + ( 1.2 + 2.3 + 3.4 +....+(n-1).n

A = (n+1).{(n-1):n+1)/2 +1/3.[1.2.3 +2.3.3 +.....+(n-1)n.3]

A = (n+1).n/2+1/3.[1.2.3 +2.3.(4-1)+ ...+(n-1).n [(n+1) - (n -2)]

A = (n+1)n/2+1/3.( 1.2.3 + 2.3.4 -1.2.3 +..+ (n-1)n(n+1)- (n-2)(n-1)n)

A =(n+1)n/2 + 1/3.(n-1)n(n+1)

A = n(n+1)[1/2 + 1/3 .(n-1)]

A = n.(n+1) \(\dfrac{3+2n-2}{6}\)

A= n.(n+1)(2n+1)/6

Bài 2 : 

a, (x+1) +(x+2) + (x+3)+...+(x+10) = 5070

    (x+10 +x+1).{( x+10 - x -1): 1 +1):2  = 5070

    (2x + 11)10 : 2 = 5070 

     ( 2x + 11)5 = 5070

      2x+ 11 = 5070:5

         2x = 1014 - 11

        2x =   1003

          x = 1003 :2

          x = 501,5 

        b, 1 + 2 + 3 +...+x = 820

           ( x + 1)[ (x-1):1 +1] : 2 = 820

           (x +1).x = 820 x 2

           (x +1).x = 1640

            (x +1) .x = 40 x 41

                 x = 40 

31x72 - 31x70 - 31 x 2 - 31

=31x(72 -70 -2 -1)

=31 x (-1)

= -31

những câu sau thì lam tương tự nha bạn ^_^