Find all ordered triples of real numbers abc with the proper

Find all ordered triples of real numbers (a,b,c) with the property that when any of the numbers is added to the product of the other two, the result is 2.

Solution

Given property \" any of the numbers is added to the product of the other two\".

the a = bc , b = ac and c = ab

Solve these equations:

we get the values of a, b and c are 1 or -1

then all ordered triples of real numbers (a,b,c) would (1, 1, 1) or (1, -1, -1) or (-1, 1, -1) or (-1, -1, 1).