Find two numbers whose sum is 26 and whose product is 165.

Let us assume that the numbers are x and
y.

Given that the sum of the numbers is
26.

==> x+ y=
26............(1)

Also, given that the product is
165.

==> x*y =
165..........(2)

We will use the substitution method to
solve for x and y.

From (1), we know that x=
26-y

Now we will substitute into
(2).

==> (26-y)*y =
165

==> 26y - y^2 =
165

==> y^2 - 26y + 165 =
0

Now we will
factor.

==> ( x-15)(x-11) =
0

==> x1= 15 ==> y1= 26-15 =
11

==> x2= 11 ==> y2= 26-11 =
15

Then, the numbers are 11 and
15.