Two numbers have sum #-37# and product #300#. What are the numbers?

1 Answer
George C.
Dec 8, 2016

#-12# and #-25#

Explanation:

The prime factorisation of #300# is:

#300 = 2^2*3*5^2#

If #m*n = 300# and #m+n = 37# then note that #37# is divisible by neither #2# nor #5#. So when splitting the factors of #300# into #m# and #n#, one of them must be divisible by #2^2 = 4# and one (possibly the same one) must be divisible by #5^2 = 25#.

We then see that #300/25 = 12# and #25+12 = 37#.

So the numbers we are looking for are #-12# and #-25#

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