Question

The product of two consecutive positive odd numbers is 575. Find the smaller of the two numbers?

Answer 1

The smaller number is 23

Explanation:

Given

Let the odd numbers be x and y [x, being the smallest]

Such that

`y = x + 2`

and

`x * y = 575`

Required

Find x

Substitute
`y = x + 2` in
`x * y = 575`

`x * [x + 2] = 575`

Open bracket

`x^2+ 2x = 575`

Equate to 0

`x^2+ 2x - 575 =0`

Expand

`x^2+ 25x -23x- 575 =0`

Factorize

`x(x+ 25) -23(x+ 25) =0`

Factor out x + 25

`(x-23) (x+ 25) =0`

Solve

`x - 23 = 0` or
`x - 25 =0`

`x= 23` or
`x = -25`

But x can't be negative.

So:

`x= 23`