Question 365893: Prove: abs(xy)= abs(x)*abs(y)
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Case 1. If one or both of x and y is/are 0, then abs(0*0) = abs(0)*abs(0) = 0, so the statement is true.
Case 2. Let x,y >0. Then xy >0, and hence abs(xy) = xy = abs(x)*abs(y).
Case 3. Let x, y<0. Then xy > 0, and hence abs(xy) = xy = abs(x)*abs(y).
Case 4. Let x >0, y<0. These imply that xy<0. Thus abs(xy) = -xy. But abs(x) = x and abs(y) = -y, and so abs(x)*abs(y) = x*(-y) = -xy. Therefore abs(xy) = abs(x)*abs(y).
Case 5. Let x<0, y>0. Argument is the same as in case 4.
The statement is completely proved.
|
|
|
