Question

Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\).CMR (a+2c)(b+d) = (a+c)(b+2d)

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

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

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

Do đó: VT=VP