SOLUTION: Find two numbers whose sum is 17 and whose squares total 145

Question 389639: Find two numbers whose sum is 17 and whose squares total 145
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The easiest way is probably to guess and check, since it is likely that both numbers will be integers. Guessing and checking, the numbers are 9 and 8.

Or, we can use and = 145. Squaring the first equation,

--> --> .

If we assume that p and q are roots of a polynomial , use Vieta's formula:

The sum of the roots is -b -->
The product of the roots is c -->

This implies b = -17 and c = 72, so p and q are roots of the polynomial . The polynomial can be factored as so p,q = (8,9).
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