Question

cho tỉ lệ thức \(\frac{a}{b}\)= \(\frac{c}{d}\)

chứng minh rằng (2008a+2009c)(b+d)=(a+c)(2008+2009d)

giúp mk nh mk đang cần gấp

Answer 1

cho tỉ lệ thức ab = cd 

chứng minh rằng (2008a+2009c)(b+d)=(a+c)(2008+2009d)

 

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

Ta có :

\(\frac{2008a+2009c}{a+c}=\frac{2008bk+2009dk}{bk+dk}=\frac{k\left(2008b+2009d\right)}{k\left(b+d\right)}=\frac{2008b+2009d}{b+d}\)

\(\Rightarrow\frac{2008a+2009c}{a+c}=\frac{2008b+2009d}{b+d}\Rightarrow\left(2008a+2009c\right)\left(b+d\right)=\left(a+c\right)\left(2008b+2009d\right)\)

=> ĐPCM

Answer 3

Ta có : \(\frac{a}{b}=\frac{c}{d}=\frac{2008a}{2008b}=\frac{2009c}{2009d}\)

\(\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{2008a}{2008b}=\frac{2009c}{2009d}=\frac{a+c}{b+d}=\frac{2008a+2009c}{2008b+2009d}\)

\(\Rightarrow\left(2008a+2009c\right).\left(b+d\right)=\left(a+c\right).\left(2008b+2009d\right)\)