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
[tex]y = x + 2[/tex]
and
[tex]x * y = 575[/tex]
Required
Find x
Substitute [tex]y = x + 2[/tex] in [tex]x * y = 575[/tex]
[tex]x * [x + 2] = 575[/tex]
Open bracket
[tex]x^2+ 2x = 575[/tex]
Equate to 0
[tex]x^2+ 2x - 575 =0[/tex]
Expand
[tex]x^2+ 25x -23x- 575 =0[/tex]
Factorize
[tex]x(x+ 25) -23(x+ 25) =0[/tex]
Factor out x + 25
[tex](x-23) (x+ 25) =0[/tex]
Solve
[tex]x - 23 = 0[/tex] or [tex]x - 25 =0[/tex]
[tex]x= 23[/tex] or [tex]x = -25[/tex]
But x can't be negative.
So:
[tex]x= 23[/tex]
