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 

\(\dfrac{16}{27}xX=\dfrac{10}{27}-\dfrac{6}{27}\)

\(\dfrac{16}{27}xX=\dfrac{4}{27}\)

\(X=\dfrac{4}{27}:\dfrac{16}{27}\)

X=\(\dfrac{1}{4}\)

16/27x X+2/9=10/27

16/27x X=10/27-2/9

16/27x X=4/27

X=4/27:16/27

X=1/4

x = 1/4

( 1 + 2 + 3 + ... + 8 + 9 + 10 ) x ( 6 x 8 - 48 )

= ( 1 + 2 + 3 + ... + 8 + 9 + 10 ) x ( 48 - 48 )

= ( 1 + 2 + 3 + ... + 8 + 9 + 10 ) x 0 = 0

=(1+2+3+.....+8+9+10) x (48-48)

=(1+2+3+.....+8+9+10) x 0

= 0

  (1 + 2 + 3 + ... + 8 + 9 + 10) x (6 x 8 - 48)

= (1 + 2 + 3 + ... + 8 + 9 + 10) x (48 - 48)

=(1 + 2 + 3 + ... + 8 + 9 + 10) x 0

= 0

1: Ta có: \(20-2\left(x+4\right)=4\)

\(\Leftrightarrow2\left(x+4\right)=16\)

\(\Leftrightarrow x+4=8\)

hay x=4

5: Ta có: \(\left(x+1\right)^3=27\)

\(\Leftrightarrow x+1=3\)

hay x=2

`#3107.101107`

`2x + 3 = -x + 6`

`\Rightarrow 2x + x = 6 - 3`

`\Rightarrow 3x = 3`

`\Rightarrow x = 3 \div 3`

`\Rightarrow x = 1`

Vậy, `x = 1.`

2x+3=-x+6

2x+x=6-3

3x=3

x=1

Ta có : x chia hết cho 60

            x chia hết cho 144

=> x thuộc BC(60;144)

Mà x nhỏ nhất khác 0 => x =BCNN(60;144)=720

Vậy x=720

\(\left(x^2+1\right)\left(x-2\right)+2x=4\Leftrightarrow x^3-2x^2+x-2+2x-4=0\Leftrightarrow x^3-2x^2+3x-6=0\Leftrightarrow\left(x-2\right)\left(x^2+3\right)=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)(do \(x^2+3\ge3>0\))

\(x(x^2+1)(x-2)+2x=4 \)

\((x^3+x)(x-2)+2x-4=0\)

\(x^4-2x^3+x^2-2x+2x-4=0\)

\(x^4-2x^3+x^2-4=0\)

\((x^4-2x^3)+(x^2-4)=0\)

\(x^3(x-2)+(x-2)(x+2)=0\)

\((x^3+x+2)(x-2)=0\)

th1:\(x^3+x+2=0 \)

              x=-1

th2 x-2=0

         x=2

ptrình cs tập nghiệm S={-1,0}

a  A=4x-x^2+3

      =(x-2)^2-1

     MIN A= -1 khi (x-2)^2=0

      x-2=0

      x=2

B=x-x^2

B=-x^2+x

-B=x^2-x

-B=(x-1/2)^2-1/4

B=-(x-1/2)^2+1/4

MAX B=1/4 khi -(x-1/2)^2=0

x-1/2=0

x=1/2

N=2x-2x^2-5

-N=2x^2-2x+5

-N=2(x^2-x+2)+1

-N=2{(x-1/2)^2+7/4}+1

-N=2(x-1/2)^2+7/2+1

-N=2(x-1/2)^2+9/2

N=-2(x-1/2)^2-9/2

MAX N=-9/2 khi -2(x-1/2)^2=0

x-1/2=0

x=1/2

a) \(\sqrt{25x}\) = 35 

b) \(\sqrt{4x}\)<= 162

 c) \(3\sqrt{x}\) = √12

 d) \(2\sqrt{x}\) >=10
 

Đùa ak :)