Question

Tìm x biết :

\(\frac{1+\frac{1+\frac{1+\frac{3}{2}}{2}}{2}}{1+\frac{2}{1+\frac{2}{1+\frac{2}{3}}}}-x=\frac{\frac{\frac{\frac{2}{3}+1}{3}+1}{3}+1}{\frac{3}{\frac{3}{\frac{3}{2}+1}+1}+1}\)

Answer 1

\(1+\frac{1+\frac{1+\frac{3}{2}}{2}}{2}=1+\frac{1+\frac{\frac{5}{2}}{2}}{2}=1+\frac{1+\frac{5}{4}}{2}=1+\frac{\frac{9}{4}}{2}=1+\frac{9}{8}=\frac{17}{8}\)

\(1+\frac{2}{1+\frac{2}{1+\frac{2}{3}}}=1+\frac{2}{1+\frac{2}{\frac{5}{3}}}=1+\frac{2}{1+\frac{6}{5}}=1+\frac{2}{\frac{11}{5}}=1+\frac{10}{11}=\frac{21}{11}\)

\(1+\frac{1+\frac{1+\frac{2}{3}}{3}}{3}=1+\frac{1+\frac{\frac{5}{3}}{3}}{3}=1+\frac{1+\frac{5}{9}}{3}=1+\frac{\frac{14}{9}}{3}=1+\frac{14}{27}=\frac{41}{27}\)

\(\frac{3}{\frac{3}{\frac{3}{\frac{3}{2}+1}+1}+1}+1=1+\frac{3}{\frac{3}{\frac{3}{\frac{5}{2}}+1}+1}=1+\frac{3}{\frac{3}{\frac{6}{5}+1}+1}=1+\frac{3}{\frac{15}{11}+1}=\frac{59}{26}\)

suy ra

\(\frac{\frac{17}{18}}{\frac{21}{11}}-x=\frac{187}{378}-x=\frac{\frac{41}{27}}{\frac{59}{26}}=\frac{1066}{1593}\Rightarrow x=-\frac{1297}{7434}\)

 

Answer 2

toàn là những bài toán khó vậy

Answer 3

\(\frac{1+\frac{1+\frac{5}{4}}{2}}{1+\frac{2}{1+\frac{6}{5}}}-x=\frac{\frac{\frac{\frac{5}{3}}{3}+1}{3}+1}{\frac{3}{\frac{\frac{3}{2}+1}{\frac{5}{2}}}+1}\)

\(\frac{1+\frac{9}{\frac{4}{2}}}{1+\frac{2}{\frac{11}{5}}}-x=\frac{\frac{\frac{14}{9}}{3}+1}{\frac{3}{1}+1}\)