Question

[Trần Thành Trung]

Cho :a+c =2b

và 1/c =1/2 (1/b + 1/d )

Chứng minh a,b,c,d lập thành 4 tỉ lệ thức.

HELP ME EVERY ONE!

THANHK YOU VERY MUCH !

Answer 1

[Sherlockichi Kudoyle]

(1) \(\frac{a+c}{2}=b\)

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

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

\(\frac{2}{c}=\frac{d}{bd}+\frac{b}{bd}=\frac{d+b}{bd}\)

\(\Rightarrow2bd=c.\left(b+d\right)\)

\(\Rightarrow2.\left(\frac{a+c}{2}\right).d=cd+cb\)

\(\Rightarrow\left(a+c\right)d=cd+cb\)

\(\Rightarrow ad+cd=cd+cb\)

\(\Rightarrow ad=cb\)

\(\Rightarrow\frac{a}{b}=\frac{c}{d}\)