SOLUTION: prove that if a product of two positive numbers is greater than their sum,then the sum is greater than four

SOLUTION: prove that if a product of two positive numbers is greater than their sum,then the sum is greater than four

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Question 894070: prove that if a product of two positive numbers is greater than their sum,then the sum is greater than four
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let a and b be the numbers.

If ab > a + b, then ab - a - b > 0 <--> (a-1)(b-1) > 1.

Let x = a-1, y = b-1. a+b > 4 if and only if x+y > 2. The problem reduces to showing that if xy > 1, then x+y > 2, however this is fairly easy to show.

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