real system

[stuart clark]

Q: Given a,b,c and d ε R satisfying a+b=8 ; ab+c+d=23 ; ad+bc = 28 ; cd = 12 , Find value of following

i) a+b+c+d =
ii) ab+cd =
iii) ac+bd =
iv) ab =

[alpercay]

I can give a solution set in Z and it is easy.One  must proof  whether there is another solution(s)  in R or not.
Using  c.d = 12  then  c = 4 , d = 3 , a = 4, b = 4 or  c = 3 , d = 4 , a = 4, b = 4
           c.d = 12  then  c = 6, d = 2 , a =3 , b = 5  or  c = 2, d = 6 , a = 5 , b = 3