Question

Cho a:b=2,6. Tìm [a,b]

Answer 1

a:b=2,6

\(\Rightarrow\frac{a}{b}=\frac{26}{10}\Leftrightarrow\frac{a}{b}=\frac{13}{5}\)

=>\(\frac{a}{13}=\frac{b}{5}\)

áp dụng t/c dãy t/s = nhau

=> \(\frac{a}{13}=\frac{b}{5}=\frac{a+b}{18}\)

=> \(\frac{18}{13}=\frac{a+b}{a}\)

=> \(\frac{18}{5}=\frac{a+b}{b}\)

=> \(\frac{a+b}{b}-\frac{a+b}{a}=\frac{18}{5}-\frac{18}{13}\)

\(\Rightarrow\frac{a\left(a+b\right)}{ab}-\frac{b\left(a+b\right)}{ab}=\frac{144}{65}\)

\(\Rightarrow\frac{\left(a+b\right)\left(a-b\right)}{ab}=\frac{144}{65}\)

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