Question

[Thư Nguyễn Nguyễn]

Cho 1/c = 1/2 (1/a+1/b)

CMR a/b = a-c / c-b

Answer 1

[Hoang Hung Quan]

Giải:

Ta có:

\(\dfrac{1}{c}=\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\)

\(\Leftrightarrow\dfrac{1}{c}\div\dfrac{1}{2}=\dfrac{1}{a}+\dfrac{1}{b}\)

\(\Leftrightarrow\dfrac{1}{c}.\dfrac{2}{1}=\dfrac{a+b}{ab}\)

\(\Leftrightarrow\dfrac{2}{c}=\dfrac{a+b}{ab}\)

\(\Leftrightarrow2ab=ac+bc\left(1\right)\)

Lại có:

\(\dfrac{a}{b}=\dfrac{a-c}{c-b}\)

\(\Leftrightarrow a\left(c-b\right)=b\left(a-c\right)\)

\(\Leftrightarrow ac-ab=ab-bc\)

\(\Leftrightarrow2ab=ac+bc\left(2\right)\)

Từ \(\left(1\right)\) và \(\left(2\right)\)

\(\Leftrightarrow\) Nếu \(\dfrac{1}{c}=\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\Leftrightarrow\dfrac{a}{b}=\dfrac{a-c}{c-b}\) (Đpcm)

Answer 2

[Thư Nguyễn Nguyễn]

cảm ơn nhá