Question

Cho \(\frac{a}{c}\)= \(\frac{b}{d}\)
Chứng minh :a)  \(\frac{a+2020b}{a-2020b}\) = \(\frac{e+2020d}{e-2020d}\)
b) \(\frac{2020\left(a+c\right)}{2020a}\)= \(\frac{b+d}{b}\)
c) 2a+3c(b+d)=(a+c)(2b+3d)
Giải giúp em nha

Answer 1

a) Áp dụng dãy tỉ số bằng nhau:

 \(\frac{a}{c}=\frac{b}{d}=\frac{2020b}{2020d}=\frac{a+2020b}{c+2020d}=\frac{a-2020b}{c-2020d}\)

=> \(\frac{a+2020b}{c+2020d}=\frac{a-2020b}{c-2020d}\)

=> \(\frac{a+2020b}{a-2020b}=\frac{c+2020d}{c-2020d}\)

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

Áp dụng dãy tỉ số bằng nhau:

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

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

=> \(\frac{2020a}{2020\left(a+c\right)}=\frac{b}{b+d}\)

=> \(\frac{2020\left(a+c\right)}{2020a}=\frac{b+d}{b}\)

c) \(2a+3c\left(b+d\right)=\left(a+c\right)\left(2b+3d\right)\)

Câu c sai đề.