Question

x/10.11 + x/11.12 +...+ x/99.100=99/100.

Answer 1

\(\dfrac{x}{10.11}+\dfrac{x}{11.12}+...+\dfrac{x}{99.100}=\dfrac{99}{100}\)

\(\Rightarrow x.\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+...+\dfrac{1}{99.100}\right)=\dfrac{99}{100}\\ \Rightarrow x.\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)=\dfrac{99}{100}\\ \Rightarrow x.\left(\dfrac{1}{10}-\dfrac{1}{100}\right)=\dfrac{99}{100}\\ \Rightarrow x.\dfrac{9}{100}=\dfrac{99}{100}\\ \Rightarrow x=\dfrac{99}{100}.\dfrac{100}{9}=11\)

Vậy x = 11