Find two consecutive positive odd integers whose product is 483.

Let the two consecutive positive odd integers be x and (x + 2).

According to the given condition,

$x(x+2)=483$

$\Rightarrow x^{2}+2 x-483=0$

$\Rightarrow x^{2}+23 x-21 x-483=0$

$\Rightarrow x(x+23)-21(x+23)=0$

$\Rightarrow(x+23)(x-21)=0$

$\Rightarrow x+23=0$ or $x-21=0$

$\Rightarrow x=-23$ or $x=21$

∴ x = 21           (x is a positive odd integer)

When x = 21,
x + 2 = 21 + 2 = 23

Hence, the required integers are 21 and 23.