what is the value of x if X + Y = 20 and X - Y = 4
Answers
If xy= 20, what are the values for X and Y?
The question does not state the relationship between X,Y and x,y . We know that xy=20 , but we are told nothing about X,Y .
If we are to make the tenuous assumption that X=x,Y=y (and we have no reason to assume that, except perhaps by further assuming that the original poster is not clear on how math notation works and erroneously thinks that consistent capitalization does not matter), then we still have problems.
If we treat x,y as natural numbers, then we have possible (x,y) pairs of (1,20),(2,10),(4,5),(5,4),(10,2) , and (20,1) . There are a total of 6 solutions.
If we treat x,y as integers, we can add (−1,−20),(−2,−10) and so on, for a total of 12 solutions.
If we treat x,y as rational numbers, then for any non-zero rational number x=ab , we can pick a y=20ba and get xy=20 . Since there are a countably infinite number of choices for x , that means there are a countably infinite number of solutions.
If we treat x,y as real numbers, then for any non-zero real number x=r , we can pick a y=20r and get xy=20 . Since there are an uncountably infinite number of choices for x , that means there an uncountably infinite number of solutions.