If a, b, c, d are positive integers such that a = bcd, b = cda, c = abd and d = abc, the value of (a + b + c + d)4/(ab + bc + ca + da)
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a = bcd
b= cda
divide both eqn
a/b = b/a
thus
a^2= b^2
a= ±b
same as b=±c
c=±d
d= ±a
a= ±b=±c=±d
a= a^3
THUS
a=1
b=1
c= 1
d=1
value of (a+b+c+d)*4/(ab+bc+ca+da)
= (1+1+1+1)*4/(1+1+1+1) = 4
b= cda
divide both eqn
a/b = b/a
thus
a^2= b^2
a= ±b
same as b=±c
c=±d
d= ±a
a= ±b=±c=±d
a= a^3
THUS
a=1
b=1
c= 1
d=1
value of (a+b+c+d)*4/(ab+bc+ca+da)
= (1+1+1+1)*4/(1+1+1+1) = 4
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