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 

Chứng minh rằng \(\frac{a}{b}=\frac{a-c}{c-b}\)

Answer 1

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

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

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

suy ra \(2ab=c\left(b+a\right)\)

\(2ab=cb+ca\)

suy ra \(ab+ab=cb+ca\)

suy a \(ab-cb=ca-ab\)

suy ra \(b\left(a-c\right)=a\left(c-b\right)\)

suy ra \(\frac{a}{b}=\frac{a-c}{c-b}\left(Đpcm\right)\)

Answer 2

chua hieu may

Answer 3

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

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

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

\(\Rightarrow2ab=c\left(b+a\right)\)

\(2ab=cb+ca\)

\(\Rightarrow ab+ab=cb+ca\)

\(\Rightarrow ab-cd=ca-ab\)

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

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

Answer 4

\(NGUY\text{ỄN}HUYHO\text{ÀNG}NH\text{ÁI}H\text{Ả}EM\)