Problem:

The numbers a,b,c and d are such that the sum of any one of them and the product of the other three is equal to 2. if a>b , a>c, and a>d, find a.

i have here my partial answer/solution:

please help me correct on this.

a+bcd =2

b+acd =2

c+abd =2

d+abc =2

by subtracting first and second equations

then,

a-b + cd(a-b) = 0 <<=--- is this correct?

(a-b) (1+cd) = 0

a -b = 0 or 1 + cd = 0

i believe a = b is rejected because a is not equal to b.

and cd is equal to - 1.

is my solution above correct.. please help.