Giải
[TEX]\left{\begin{a+c=2b}\\{2bc = c(b+d)} [/TEX]
[TEX]\Leftrightarrow\left{\begin{d(a+c)=2bd}(1)\\{2bc = c(b+d)(2)} [/TEX]
Vì [TEX]a;b#0[/TEX]nên ta lấy [TEX](1)[/TEX]chia [TEX](2)[/TEX]
Ta được:
[TEX]\frac{2bc}{2bd}=\frac{c(b+d)}{d(a+c)}[/TEX]
[TEX]\Leftrightarrow\frac{c}{d}=\frac{c(b+d)}{d(a+c)}[/TEX]
Mặt khác
[TEX]c(b+d)=d(a+c)[/TEX]
[TEX]\Leftrightarrow\frac{a+c}{c}=\frac{b+d}{d}[/TEX]
[TEX]\Leftrightarrow\frac{a}{b}=\frac{c}{d}[/TEX]
Nhớ thanks nha!!!