Question

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

Answer 1

Answer:

The smaller number is 23

Step-by-step 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:

$x= 23$