Question

[Viet Anh]

Cho a/b=c/d.Chứng minh rằng (a+2c)(b+d)=(a+c)(b+2d)

Answer 1

[Phong Thần]

Ta thấy : b/a = d/c ⇒ad = bc (1)

Ta có: (a+2c)(b+d)=(a+c)(b+ad)

<=> ab+ad+2bc+2cd=ab+2ad+bc+2cd

<=> ab+ad+2bc+2cd-ab-2ad-bc-2cd=0

<=>-ad+bc=0<=>bc-ad=0<=>ad=bc=>(1) luôn đúng

=>ĐFCM