Question

cho \(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\) VỚI a,b,c khác 0;b khác c

CMR \(\frac{a}{b}=\frac{a-c}{c-b}\)

Answer 1

hoàng thái giám

Answer 2

Ta có:\(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)

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

\(\Rightarrow\frac{2}{c}=\frac{b}{a.b}+\frac{a}{a.b}\)

\(\Rightarrow\frac{2}{c}=\frac{a+b}{a.b}\)

\(\Rightarrow2.a.b=c\left(a+b\right)\)

\(\Rightarrow a.b+a.b=ca+cb\)

\(\Rightarrow ab-cb=ac-ab\)

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

\(\Rightarrow\frac{a}{b}=\frac{a-c}{c-b}\left(đpcm\right)\)

hok tốt!!