Question

[Long Phan]

cho 1/c=1/2(1/a+1/b).cmr a/b=(a-c)/(c-b)

Answer 1

[Nguyệt]

\(\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{a}+\frac{1}{b}\right)\Rightarrow\frac{1}{c}=\frac{a+b}{2ab}\Rightarrow c=\frac{2ab}{a+b}\)

\(\frac{a-c}{c-b}=\frac{a-\frac{2ab}{a+b}}{\frac{2ab}{a+b}-b}=\frac{\frac{ab-a^2}{-b-a}}{\frac{b^2-ab}{-b-a}}=\frac{a.\left(b-a\right)}{b.\left(b-a\right)}=\frac{a}{b}\left(đpcm\right)\)

p/s: cách thủ công thôi ak, ai có cách hay làm nha =))