The product of two consecutive positive integers is 812. What is the value of the lesser integer?

Solution:

Let, the two consecutive positive integers be x and (x + 1).

Given, x(x + 1) = 812

x² + x - 812 = 0

Splitting the middle term

x² + 29x - 28x - 812 = 0

Taking out the common terms

x(x + 29) - 28(x + 29) = 0

(x - 28)(x + 29) = 0

Here,

⇒ x - 28 = 0

x = 28

⇒ x + 29 = 0

x = -29

Since, the integer is positive the value of x is 28.

Next consecutive integer is (x + 1) = 28 + 1 = 29

Therefore, the two consecutive positive integers are 28 and 29.

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The product of two consecutive positive integers is 812. What is the value of the lesser integer?

Summary:

The product of two consecutive positive integers is 812. The value of the lesser integer is 28.