# 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 ?

Algebra ->  Algebra  -> Numeric Fractions Calculators, Lesson and Practice -> 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 ?       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Numeric Fractions Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Numeric Fractions 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(4)   (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.