The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?
Answer: 9, 10
Explanation
Let the two consecutive positive integers be x and x + 1
x2 + (x + 1)2 - x(x + 1) = 91
x2 + x - 90 = 0
(x + 10)(x - 9) = 0 => x = -10 or 9.
As x is positive x = 9
Hence the two consecutive positive integers are 9 and 10.
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