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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


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


Grade:12

1 Answers

Pulkit Singhal
25 Points
10 years ago

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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