Question 153153
Let one number be x, then the other one can be expressed as x + 2.
As their product is 10, we have
x(x + 2) = 10
expanding the left side, we have
{{{x^2 + 2x = 10}}}

Completing square, we have
{{{x^2 + 2x + 1 = 1 + 10}}}
{{{(x + 1)^2 = 11}}}
{{{x = -1+- sqrt(11) }}}
So
{{{x = -1+sqrt(11)}}} or {{{x = -1-sqrt(11)}}}
So there are two solution to this problem:
(1)
one number is {{{x = -1+sqrt(11)}}}.
The other is {{{x+2 = -1+sqrt(11)+2=1+sqrt(11)}}}
(2)
one number is {{{x = -1-sqrt(11)}}}
the other is {{{x+2 = -1-sqrt(11)+2=1-sqrt(11)}}}