Question

If a,b,c,d are natural such that a=bc, b=cd, c=da, d=ab then (a+b)(b+c)(c+d)(d+a)=?

Answer 1

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if a,b,c,d are natural numbers,and a=bc,b=cd,c=da and d=ab then (a+b)(b+c)(c+d)(d+a)=

0

Home » Forum » Algebra » if a,b,c,d are natural numbers,and...

if a,b,c,d are natural numbers,and a=bc,b=cd,c=da and d=ab then (a+b)(b+c)(c+d)(d+a)=

multiplying all;abcd=1

a/b=bc/cd

a/b=b/d d=ab

a*ab=b^2

a^2=b

By substituting equation ,

d=a^3

c=a^4

b=a^2

a=a

multiplying these all

abcd=a^10

as we have earlier

abcd=1

1=a^10

a=1

b=1

c=1

d=1

solution=

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