Question

Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. find the middle number.

Answer 1

Middle number can be any whole number...

Answer 2

The value of the middle term is 1.

Given:

3 consecutive numbers such that the square of the middle term is greater than the product of the other 2 by 1

To Find:

the value of the middle number

Solution:

let the 3 numbers be x, (x + 1), and (x + 2)

thus, the middle number (x + 1)

so, we get the following equation-

(x + 1)² - x(x + 2) = 1

x² + 1 + 2x - x² + 2x = 1

4x + 1 = 1

4x = 0

x = 0

⇒ (x + 1) = 1

Thus, the value of the middle term is 1.

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