Question

cho \(\frac{a}{b}\)=\(\frac{c}{d}\) CMR

A)\(\frac{3a-2c}{3b+2d}\)= \(\frac{2a+5c}{2b+5d}\) 

B)\(\frac{a^3}{b^3}\) =\(\frac{\left(a+c\right)^3}{\left(b+d\right)^5}\)

Answer 1

Đặt 

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

a)

Sửa đề nhá : 

\(\frac{3a+2c}{3b+2d}=\frac{3bk+2dk}{3b+2d}=\frac{k\left(3b+2d\right)}{\left(3b+2d\right)}=k\)(1)

\(\frac{2a+5c}{2b+5d}=\frac{2bk+5dk}{2b+5d}=\frac{k\left(2b+5d\right)}{2b+5d}=k\)(2)

Từ (1) và (2) 

=> \(\frac{3a+2c}{3b+2d}=\frac{2a+5c}{2b+5d}\)

b)

\(\frac{a^3}{b^3}=\frac{b^3k^3}{b^3}=k^3\)(3)

\(\frac{\left(a+c\right)^3}{\left(b+d\right)^3}=\frac{\left(bk+dk\right)^3}{\left(b+d\right)^3}=\frac{k^3\left(b+d\right)^3}{\left(b+d\right)^3}=k^3\)(4)

Từ (3) và (4) 

=> \(\frac{a^3}{b^3}=\frac{\left(a+c\right)^3}{\left(b+d\right)^3}\)