Question

If (a2 + c2

)(b2 + d2

) = (ab + cd)2

, then ad - bc =​

Answer 1

Step-by-step explanation:

Let f(x)=x+1x . f(x) is defined for x≠0 . It is not difficult to prove that if f(x)=f(y) then either y=x or y=1x . Now (a2+b2)/(c2+d2)=ab/cd , if a,b,c,d≠0 , can be rewritten as f(ab)=f(cd) . So it follows from the remark above that either ab=cd or ab=dc . If a=b=0 and c,d≠0 , the equality holds as well, but in this case it does not follow that a:b=c:d , however it does follow that a:c=b:d