Question

cho a+c=2b va 2.bd=(b+d).c 

Chứng minh a/b=c/d

 

Answer 1

\(2bd=\left(2b\right)d=\left(b+d\right)c=bc+cd\)

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

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

\(\Rightarrow ab=bc\)

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

Answer 2

Ta có :

a + c = 2b         (1)

2bd = c.(b+d)     (2)

Thế (1) vào (2) , ta được;

(a+c).d = c.(b+d)

Thao tính chất phân phối, ta có:

ad + cd = cb + cd.

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

Answer 3

\(2bd=\left(b+d\right).c=>\left(a+c\right).d=\left(b+d\right).c=>ad+cd=bc+cd\)

\(=>ad=bc=>\frac{a}{b}=\frac{c}{d}\left(đpcm\right)\)