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

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Let one of the numebrs be x and the other number is y :

Given that the sum of the numbers equal 26:

==> x + y = 26

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

Also, given that the product of the numbers = 165.

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

Let us substitue (1) in (2):

==> x*y = 165

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

==> 26y - y^2 = 165

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

\Let us factor the equation:

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

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

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

**Then the numbers are 11 and 15 **

The product of two numbers is 165. So let the two numbers be x and 165/x .

Then since their sum is 26, x+165/x = 26.

We multiply both sides of the quation x+165/x = 26 by x.

x^2+165= 26x.

x^2-26x +165 = 0.

( x-13)^2 - 13^2 +165 = 0

(x-13)^2 = 169-165 = 4.

(x-3)^2 = 4.

x-13 = 2 or -2.

x = 13+2 = 15. or x = 13-2 = 11.

Therefore the two numbers are 13 and 11.