Question 1132277
Try pairs of factors of 66.
Should take less than 10 seconds to find them.
===================
Copied from the other tutor's solution:
------------
------------
1) i +j = 17
:
2) ij = 66
:
solve equation 1 for i
:
i = 17 -j
:
substitute for i in equation 2
:
(17 -j)j = 66
:
17j -j^2 = 66
:
j^2 -17j +66 = 0
At this point, you find a pair of factors of 66 with a sum of 17.  Similar to "going around the barn to get to the door."
--------
But, if they're not integers, eg, the sum is 17 and the product is 65:
---
1) i +j = 17
:
2) ij = 65
:
i = 17 -j
:
j^2 -17j +65 = 0
:
(17 -j)j = 65
:
17j -j^2 = 65
j^2 - 17j + 65 = 0
*[invoke solve_quadratic_equation 1,-17,65]
-----
j =~ 11.19 or 5.8