Question

Prove or disprove that max(x,y) = 1/2(x + y + (x - y) ), where x and y are real numbers

Answer 1

The equation max(x,y) = 1/2(x + y + (x - y)) holds true for all real numbers x and y.

Step-by-step explanation:

To prove or disprove the equation max(x,y) = 1/2(x + y + (x - y)), we need to consider the cases where x is greater than or equal to y and where y is greater than x.

Case 1: x >= y

In this case, the equation becomes max(x,y) = 1/2(x + y + (x - y)) = max(x,y) = 1/2(x + y + x - y) = max(x,y) = 1/2(2x) = max(x,y) = x. So, the equation holds true when x >= y.

Case 2: y > x