The product of two consecutive positive integers is 55 more than their sum. Find the integers.

Solution:

Given that two consecutive positive integers is 55 more than their sum

Let the two consecutive positive numbers be x and x + 1

x(x + 1) = 55 + x + x + 1

x(x + 1) = 56 + 2x

x² + x = 56 + 2x

x² + x - 2x - 56 = 0

x² - x - 56 = 0

x² - 8x + 7x - 56 = 0 [By splitting the terms and solving the quadratic equation]

x(x - 8) + 7(x - 8) = 0

(x - 8)(x + 7) = 0

x= 8, -7

As integer should be positive, we can neglect -7

Therefore, the required integers are 8 and 9.

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The product of two consecutive positive integers is 55 more than their sum. Find the integers.

Summary:

The product of two consecutive positive integers is 55 more than their sum, then the integers are 8, 9.