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