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If a,b,c,d are positive integers such that a =bcd ,b=cda.c=dab and d= abc then find the value of (a+b+c+d)^4/(ab+bc+cd+da)^2
a=bcd (1)
b=cda (2)
c=dab (3)
d=abc (4)
On dividing equation 1 by 2 we get
a/b = bcd/cda
a/b = b/a
a2 = b2
On taking sqrt both the sides
a = b
On solving other equation we get a=b=c=d
(a+b+c+d)4 / (ab+bc+cd+da)2 = (a+a+a+a)4 / (a2+a2+a2+a2)2
= (4a)4 / (4a2)2 = 256a4 / 16a4 = 16
Hence answer is 16
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