# The product of two consecutive integers is 98 more than the next integer. What is the largest of the three integers?

So the three integers are

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Let's denote the first integer as ( x ) and the next consecutive integer as ( x + 1 ). According to the given information, the product of these two consecutive integers is ( 98 ) more than the next integer, which can be expressed as:

[ x(x + 1) = (x + 1) + 98 ]

Solving this equation:

[ x^2 + x = x + 99 ] [ x^2 = 99 ] [ x = \sqrt{99} ]

Since we're looking for integers, the largest integer that is less than or equal to ( \sqrt{99} ) is ( 9 ). So, the largest of the three integers is ( x + 1 = 9 + 1 = 10 ).

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