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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

 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...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

 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

Approved by eNotes Editorial Team