SOLUTION: if a,b,c and d are in set of natural numbers(N) with a=bcd, b=cda and d=abc then,what is the value of (a+b+c+d)^2 ?

Question 479514: if a,b,c and d are in set of natural numbers(N) with a=bcd, b=cda and d=abc then,what is the value of (a+b+c+d)^2 ?

Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!

Since and , we can substitute b into the first equation and obtain , which can be simplified into . Since a,b,c,d are natural numbers (not equal to zero), we can divide both sides of the last equation by a and obtain . Again, using the fact that a,b,c,d are natural numbers we conclude that both c and d are equal to 1.
Now we have to find values of a and b. We can use the last equation and substitute c = 1 and d = 1 to obtain . Again, a and b are natural numbers, and thus both equal to 1. So, the only solution to the system of equations for a,b,c,d among the set of natural numbers is all of the being equal to 1.
Thus is equal to 16.
RELATED QUESTIONS
A, B, C, and D, are distinct digits, and 4(AAB) = CDA. If C is less than d, find the sum (answered by ikleyn)

A, B, C, and D are distinct digits, and 4xAAB=CDA. If C is less than D, find the sum... (answered by greenestamps)

A, B, C and D are distinct digits, and 4 x AAB = CDA. If C is less than D, find the sum... (answered by ikleyn)

In triangle ABC, side AC is extended through C to point D to create external angle BCD.... (answered by ankor@dixie-net.com)

if a+b+c+d=2001 and b+d=2002, what is the value of... (answered by orca)

This is a Number Theory proof: If N = abc + 1, prove that (N, a) = (N, b) = (N, c) =... (answered by KMST)

1) A warehouse contains 200 shoes of size 8, 200 shoes of size 9 and 200 shoes of size... (answered by psbhowmick)

The set of natural numbers less than 10. A. 510;511 B. 511;512 C. 511;510 D.... (answered by ikleyn,josgarithmetic)

If C is 6, and d is 1/6, then what is the value of c expressed in terms of d? Answer... (answered by rothauserc)