SOLUTION: If 0 < x < 1 , 0 < y < 1 prove that 0 < x + y

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Question 1118504: If 0 < x < 1 , 0 < y < 1 prove that 0 < x + y - xy < 1
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

x and y are both positive and less than 1; that means the product xy is less than x and less than y.

So the expression x + y - xy is always positive; i.e., the inequality

is always true.

To prove the other inequality

rewrite the statement to be proved as

Then

Because x and y are both between 0 and 1, one of those factors is always negative and the other is always positive, so the product is always negative.

So the second inequality is also always true, making the original compound inequality always true.

SOLUTION: If 0 < x < 1 , 0 < y < 1 prove that 0 < x + y - xy < 1