Question

Cho (a+b+c+d).(a-b-c+d)=(a-b+c-d).(a+b-c-d)

     Chứng minh \(\frac{a}{b}=\frac{c}{d}\)

Answer 1

ta có: (a+b+c+d).(a-b-c+d)=(a-b+c-d).(a+b-c-d)
<=> a²-ab-ac+ad+ab-b²-bc+bd+ac-bc-c²+cd+ad-bd-cd+d²=a²+ab-ac-ad-ab-b²+bc+bd+ac+bc-c²-cd-ad-bd+cd+d²
<=> a²-b²-c²+d²+2ad-2bc=a²-b²-c²+d²-2ad+2bc
<=> 2ad-2bc=-2ad+2bc
<=> ad=bc
<=> a/b = c/d (dpcm)