\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5070.\)

\(\left(x+x+x+x+....+x\right)+\left(1+2+3+....+100\right)=5070\)

\(100x+101.100:2=5070\)

\(100x+5050=5070\)

\(100x=5070-5050=20\)

\(x=20:100=\frac{20}{100}=\frac{2}{10}=\frac{1}{5}=0,2\)

0,2 nhé bạn

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 

\(D=x^2-x+1=\left(x^2-x+\frac{1}{4}\right)+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)

Vậy GTNN của D là \(\frac{3}{4}\)khi x = \(\frac{1}{2}\)

\(E=x\left(x-3\right)=x^2-3x=\left(x^2-3x+\frac{9}{4}\right)-\frac{9}{4}=\left(x-\frac{3}{2}\right)^2-\frac{9}{4}\ge-\frac{9}{4}\)

Vậy GTNN của E là \(-\frac{9}{4}\)khi x = \(\frac{3}{2}\)

\(G=x^2+5y^2+2xy-2y+100\)

\(G=\left(x^2+2xy+y^2\right)+\left(4y^2-2y+\frac{1}{4}\right)+\frac{399}{4}\)

\(G=\left(x+y\right)^2+\left(2y-\frac{1}{2}\right)^2+\frac{399}{4}\ge\frac{399}{4}\)

Vậy GTNN của G là \(\frac{399}{4}\)khi x = \(-\frac{1}{4}\); y = \(\frac{1}{4}\)

Hihiii cam on bann nhieuu nhe <3

a) \(5^x=100\)

\(5^x=10^2=\left(5\cdot2\right)^2\)

Sai đề

b) \(219-2^x=77\)

\(219-77=2^x\)

\(142=2^x\)??

c) \(18\left(x+27\right)=360\)

\(x+27=\frac{360}{18}=20\)

\(x=20-27=-7\)

d)\(\frac{\left(7x-140\right)}{21}=49\Rightarrow7x-140=49\cdot21=1029\)

\(7x=140+1029\)

\(7x=1169\Rightarrow x=\frac{1169}{7}=167\)

e) \(350+3^x=470\Rightarrow3^x=470-350=120\)

\(3^x=120????\)

5 câu sai hết 3 câu :|

Dũng Lê Trí bạn sai thì có dấu * là dấu nhân mà

(x+1)+(x+2)+................+(x+100)=205550

=>x+1+x+2+................+x+100=205550

=>100x+(1+2+3+...........+100)=205550

=>100x+5050=205550

=>100x=205550-5050

=>100x=200500

=>x=200500:100

=>x=2005

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + .... + ( x + 100 ) = 205550

=> x + 1 + x + 2 + x + 3 + .... + x + 100 = 205550

=> ( x + x + x + .... + x ) + ( 1 + 2 + 3 + .... + 100 ) = 205550

=> 100x + { [ 100 . ( 100 + 1 ) ] : 2 } = 205550

=> 100x + [(  100 . 101 ) : 2 ] = 205550

=> 100x + ( 10100 : 2 ) = 205550

=> 100x + 5050 = 205550

=> 100x = 205550 - 5050

=> 100x = 200500

=> x = 200500 : 100

=> x = 2005

Vậy x = 2005

cach lam ai dung ,

a) 2-(x+3) = 1+2+3+...+99

1+2+3+...+99 → có 99 số hạng

2-(x+3) = (1+99).99 : 2 

2-(x+3) = 4950

x+3 = 2 + 4950 

x+3 = 4952

x = 4952 - 3

x = 4949

b) (x+1)+(x+2)+...+(x+100) = 5750

→ có 100 cặp

(x+x+x+...+x) + ( 1+2+3+...+100 ) = 5750

=> 100x + 5050 = 5750

100x = 5750 - 5050

100x = 700

x = 700 : 100

x = 7

 0o0 Nguyễn Đoàn Tuyết Vy 0o0 bà kêu tui học tốt có nghĩa là học giốt đúng ko

b)(x+1)+(x+2)+(x+3)+(x+4)+...............+(x+100)=5750

(x+x+x+x+...+x) + (1+2+3+4+...+100) = 5750

     100x             +           5050           = 5750

                       100x                          = 5750 - 5050

                       100x                          = 700

                         x                             = 700 : 100

                         x                             = 7

Vậy ...