10 x (  X - 2 ),x X + 2 = 220

10 . x .( x - 2) = 220 - 2

10x^2 - 20x    = 218 

 10x^2 - 20x - 218 = 0 

d: ĐKXĐ: x<>-4; x<>-5; x<>-6; x<>-7

\(PT\Leftrightarrow\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}+\dfrac{1}{x+6}-\dfrac{1}{x+7}=\dfrac{1}{18}\)

=>\(\dfrac{1}{x+4}-\dfrac{1}{x+7}=\dfrac{1}{18}\)

=>\(\dfrac{x+7-x-4}{\left(x+4\right)\left(x+7\right)}=\dfrac{1}{18}\)

=>x^2+11x+28=54

=>x^2+11x-26=0

=>(x+13)(x-2)=0

=>x=2 hoặc x=-13

e: \(\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}=10\)

\(\Leftrightarrow\left(\dfrac{x-241}{17}-1\right)+\left(\dfrac{x-220}{19}-2\right)+\left(\dfrac{x-195}{21}-3\right)+\left(\dfrac{x-166}{23}-4\right)=0\)

=>x-258=0

=>x=258

Số số hạng là (20-1):1+1=20(số)

Tổng của dãy số từ 1 đến 20 là: 

\(\dfrac{20\cdot\left(20+1\right)}{2}=10\cdot21=210\)

\(x+1+x+2+...+x+20=220\)

=>\(10x+210=220\)

=>10x=10

=>x=1

\(\left(x^2+3^2\right).10+90=220\\ \Rightarrow\left(x^2+9\right).10=130\\ \Rightarrow x^2+9=13\\ \Rightarrow x^2=4\\ \Rightarrow x^2=2^2\\ \Rightarrow x=2.\)

Cần ghi rõ dấu.

dấu ^ là mũ

\(\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}=10\)

\(\Leftrightarrow\dfrac{x-241}{17}+\dfrac{x-220}{19}+\dfrac{x-195}{21}+\dfrac{x-166}{23}-10=0\)

\(\Leftrightarrow(\dfrac{x-241}{17}-1)+(\dfrac{x-220}{19}-2)+(\dfrac{x-195}{21}-3)+(\dfrac{x-166}{23}-4)=0\)

\(\Leftrightarrow\dfrac{x-258}{17}+\dfrac{x-258}{19}+\dfrac{x-258}{21}+\dfrac{x-258}{23}=0\)

\(\Leftrightarrow\left(x-258\right)\left(\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{23}\right)=0\)

\(Do\) \(\left(\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{21}+\dfrac{1}{23}\right)\ne0\) \(nên\) \(để\) \(gt=0\)

\(\Leftrightarrow x-258=0\)

\(\Leftrightarrow x=258\)

\(Vậy...\)