With questions like these it is usually best to just guess and check and move on. So they are asking for two consecutive integers where their product is greater than their sum. Just start with 1 and 2. Notice this does not satisfy the conditions given since 1 x 2 = 2 and 1 + 2 = 3. The next set of consecutive integers does satisfy the conditions because 2 x 3 = 6 and 2 + 3 = 5. The same thing applies for every single other set of consecutive positive integers except for 1 and 2 so there are infinite answers x and y such that x does not equal 1 and y = x + 1 with both x and y contained in the Natural numbers (if N doesn't contain 0). Or you could do x(x + 1) > 2x + 1. Then x^2 + x >2x + 1 and then solve from there. Hope this helps!
Apr 28th, 2015
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