The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

Quadratic Equations 30/09/2021

A. 9, 10
B. 10, 11
C. 11, 12
D. 12, 13

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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