\(S=\frac{1}{x^2+5x+4}+\frac{1}{x^2+11x+28}+\frac{1}{x^2+17x+70}+\frac{1}{x^2+23x+130}+\frac{1}{x^2+29x+208}\)

\(=\frac{1}{x^2+4x+x+4}+\frac{1}{x^2+7x+4x+28}+...+\frac{1}{x^2+16x+13x+208}\)

\(=\frac{1}{x\left(x+4\right)+\left(x+4\right)}+\frac{1}{x\left(x+7\right)+4\left(x+7\right)}+...+\frac{1}{x\left(x+16\right)+13\left(x+16\right)}\)

\(=\frac{1}{\left(x+1\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+7\right)}+...+\frac{1}{\left(x+13\right)\left(x+16\right)}\)

\(=\frac{1}{3}\left[\frac{3}{\left(x+1\right)\left(x+4\right)}+\frac{3}{\left(x+4\right)\left(x+7\right)}+...+\frac{3}{\left(x+13\right)\left(x+16\right)}\right]\)

\(=\frac{1}{3}\left[\frac{1}{x+1}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+7}+...+\frac{1}{x+13}-\frac{1}{x+16}\right]\)

\(=\frac{1}{3}\left[\frac{1}{x+1}-\frac{1}{x+16}\right]\)\(=\frac{1}{3}\left[\frac{x+16}{\left(x+1\right)\left(x+16\right)}-\frac{x+1}{\left(x+1\right)\left(x+16\right)}\right]\)

\(=\frac{1}{3}\cdot\frac{15}{x^2+17x+16}=\frac{5}{x^2+7x+16}\)

Bài 1: 

\(=\dfrac{1}{\left(x+1\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+10\right)}+\dfrac{1}{\left(x+10\right)\left(x+13\right)}+\dfrac{1}{\left(x+13\right)\left(x+16\right)}\)

\(=\dfrac{1}{3}\left(\dfrac{3}{\left(x+1\right)\left(x+4\right)}+\dfrac{3}{\left(x+4\right)\left(x+7\right)}+\dfrac{3}{\left(x+7\right)\left(x+10\right)}+\dfrac{3}{\left(x+10\right)\left(x+13\right)}+\dfrac{3}{\left(x+13\right)\cdot\left(x+16\right)}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+7}+\dfrac{1}{x+7}-\dfrac{1}{x+10}+\dfrac{1}{x+10}-\dfrac{1}{x+13}+\dfrac{1}{x+13}-\dfrac{1}{x+16}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+16}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{x+16-x-1}{\left(x+1\right)\left(x+16\right)}=\dfrac{5}{\left(x+1\right)\left(x+16\right)}\)

Bài 2: 

\(\Leftrightarrow a^2-2a+1+b^2+4b+4+4c^2-4c+1=0\)

\(\Leftrightarrow\left(a-1\right)^2+\left(b+4\right)^2+\left(2c-1\right)^2=0\)

Dấu '=' xảy ra khi a=1; b=-4; c=1/2

D

D

D

540

279,9036

   0,54  x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18

= 0,54 x 550 + ( 0,27 x 2 ) x 126 + ( 3 x 0,18 ) + 324

= 0,54 x 550 + 0,54  x 126 + 0,54 x 324 

= 0,54 x ( 550 + 126 + 324 )

= 0,54 x 1000

= 540

540

   0,54  x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18

= 0,54 x 550 + ( 0,27 x 2 ) x 126 + ( 3 x 0,18 ) + 324

= 0,54 x 550 + 0,54  x 126 + 0,54 x 324 

= 0,54 x ( 550 + 126 + 324 )

= 0,54 x 1000

= 540

vừa làm rồi

a: =1300

b: =402x2=804

130 x 2 + 130 x 8
= 130 x (2+8)
= 130 x 10
= 1300
402 x 9 – 402 x 7
= 402 x (9-7)
= 402 x 2
= 804

Mik không hiểu cái đề bài @@

Với sao x + ( x+ 1 ) + ( x + 2 ) Vậy thì các giá trị trong ngoặc sau có x không tkế ???

đề sai sai hay sao ấy !