Question

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

CMR : (a + 2c).(b+d) = (a+c).(b+2d)

Answer 1

ta có: \(\frac{a}{b}=\frac{c}{d}=k\)

\(\Rightarrow\frac{a}{b}=k\Rightarrow a=bk\)

\(\frac{c}{d}=k\Rightarrow c=dk\)

thay vào \(\left(a+2c\right).\left(b+d\right)=\left(bk+2dk\right).\left(b+d\right)=k.\left(b+2d\right).\left(b+d\right)\)

\(\left(a+c\right).\left(b+2d\right)=\left(bk+dk\right).\left(b+2d\right)=k.\left(b+d\right).\left(b+2d\right)\)

\(\Rightarrow\left(a+2c\right).\left(b+d\right)=\left(a+c\right).\left(b+2d\right)\left(=k.\left(b+2d\right).\left(b+d\right)\right)\)( đ p c m)

CHÚC BN HỌC TỐT!!!!!!!!

Answer 2

Ta có:

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

\(ab+ad+2cb+2cd=ab+2ad+cb+2cd\)

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