a,  (x-10)^2-x(x+80) 

=x²-20x+100-x²-80x

=-100x+100

Thay x=0,98 

=-100.0,98+100

=2

 b, (2x+9)^2-x(4x+31)

=4x²+36x+81-4x²-31x

=5x+81

Thay x=16,2

=5.16,2+81

=162

c,  4x^2-28x +49 

=(2x)²-2.2x7+7²

=(2x-7)²

Thay x=4

=(2.4-7)²

=1²

=1

  đ, x^2-9x^2+27x-27

 =k bt lm

LÀM ƠN GIÚP MIK ĐI MÀ, NĂN NỈ CÁC BẠN ĐÓ!!!!!!!!!!!!!!!!!!!!!!

a) \(\frac{14}{15}:\frac{9}{10}=x:\frac{3}{7}\Rightarrow\frac{28}{27}=x:\frac{3}{7}\Rightarrow x=\frac{4}{9}\)

b) \(\left(x-\frac{4}{7}\right)^3=343\Rightarrow\left(x-\frac{4}{7}\right)^3=7^3\Rightarrow x-\frac{4}{7}=7\Rightarrow x=\frac{53}{7}\)

c) \(x^5=x^3\Leftrightarrow\hept{\begin{cases}x=1\\x=0\end{cases}}\)

e) \(\left(x-1\right)^4=16\Leftrightarrow\orbr{\begin{cases}\left(x-1\right)^4=2^4\\\left(x-1\right)^4=\left(-2\right)^4\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x-1=2\\x-1=\left(-2\right)\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}\)

\(\frac{x}{27}-\frac{2}{9}=\frac{6}{18}\)

\(\frac{x}{27}=\frac{3}{9}+\frac{2}{9}\)

\(\frac{x}{27}=\frac{5}{9}\)

\(\frac{x}{27}=\frac{15}{27}\)

=> x = 15

=.>X/27-6/27=6/18

=> (X-6)/27=6/18

=>(2X-12)/54=18/54

=> 2X-12=18

=> 2X=30

=>X=15

VẬY X=15

\(\frac{x}{27}-\frac{2}{9}=\frac{6}{18}\)

\(\Rightarrow\frac{x}{27}=\frac{1}{3}+\frac{2}{9}\)

\(\Rightarrow\frac{x}{27}=\frac{5}{9}\)

\(\Rightarrow\frac{x}{27}=\frac{5.3}{9.3}\)

\(\Rightarrow\frac{x}{27}=\frac{15}{27}\)

\(\Rightarrow x=15\)

~Study well~

#SJ

đề bài sai sao ý 9/15 mà nếu 9/ 16 thì ko tính thận tiện đc

\(\dfrac{10}{15}\)x\(\dfrac{9}{16}+\dfrac{7}{15}\)x\(\dfrac{10}{15}\)

=> \(\dfrac{10}{15}\)x\(\left(\dfrac{9}{16}+\dfrac{7}{15}\right)\)

=> \(\dfrac{10}{15}\)x\(\dfrac{247}{240}\)

=> \(\dfrac{247}{360}\)

1. Tìm x

a) 1+2+3+...+x = 210

=> \(\frac{x\left(x+1\right)}{2}=210\)

=> x = 20

b) \(32.3^x=9.3^{10}+5.27^3\)

=>\(32.3^x=9.3^{10}+5.3^9\)(\(27^3=\left(3^3\right)^3=3^9\))

=>\(32.3^x=9.3.3^9+5.3^9\)

=>\(32.3^x=3^9\left(9.3+5\right)\)

=>\(32.3^x=3^9.32\)

=>x = 9

2.

Ta có 2A = 3A - A

=> 2A = \(3\left(1+3+3^2+3^3+....+3^{10}\right)\)\(-\)\(1-3-3^2-3^3-....-3^{10}\)

=> 2A = \(3+3^2+3^3+.....+3^{11}-\)\(1-3-3^2-3^3-...-3^{10}\)

=> 2A = \(3^{11}-1\)

=> 2A+1 = \(3^{11}-1+1\)=\(3^{11}\)

=> n = 11

Ta có : a)1 + 2 + 3 + ... + x = 210

=> \(\frac{x\left(x+1\right)}{2}=210\)

=> x(x + 1) = 420

=> x(x + 1) = 20.21

=> x = 20

1/ 

a) \(1+2+3+...+x=210\)

\(\Rightarrow\frac{x.\left(x+1\right)}{2}=210\)

\(\Rightarrow x.\left(x+1\right)=210.2=420\)

\(\Rightarrow x^2+x=420\)

\(\Rightarrow x^2+x=400+20=20^2+20\Leftrightarrow x=20\)

b) \(32.3^x=9.3^{10}+5.27^3\)

\(\Rightarrow32.3^x=629856\)

\(\Rightarrow3^x=629856:32=19683=3^9\)

\(\Rightarrow x=9\)

2/

\(A=1+3+3^2+3^3+...+3^{10}\)

\(\Rightarrow A=3^0+3^1+3^2+3^3+...+3^{10}\)

\(\Rightarrow A=\frac{3^{10+1}-1}{3-1}=88573\)

Tìm n:

\(2.A+1=3^n\Rightarrow2.88573+1=3^n\)

\(\Rightarrow177147=3^n\Leftrightarrow3^{11}=3^n\Leftrightarrow n=11\)

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