The two of the consecutive positive integers whose product is 17 more than 5 times their sum are 11 and 12.
What are Integers?
An integer is a complete number, therefore, not including the decimals and fractions. And it that can be either positive, negative, or zero.
Integer examples include -5, 1, 5, 8, 97, and 3,043.
Non-integer numbers include: -1.43, 1 3/4, 3.14, and more.
Let the first of the two consecutive integers be represented by x. Then, the other number can be written as (x+1).
Now, the product and the sum of the two numbers can be written as,
Product = x(x+1) = x² + x
Sum = x + (x+1) = 2x + 1
Further, it is given that the product of two consecutive positive integers is 17 more than 5 times their sum. Therefore, we can write,
x² + x = 17 + 5(2x + 1)
x² + x = 17 + 10x + 5
x² + x - 17 - 10x - 5 = 0
x² - 9x - 22 = 0
x² - 11x + 2x - 22 = 0
x(x - 11) + 2(x - 11) = 0
(x - 11)(x + 2) = 0
x = -2, 11
Thus, there are two numbers that can fulfil the given condition but since it is mentioned that we only need two positive consecutive integers. Therefore, the two numbers are 11 and 12.
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