Posted by Omar on Wednesday, February 13, 2013 at 2:15pm.
Find all pairs of numbers such that when they are added they equal 100, and when
they are multiplied they are at least 2000.

math  Steve, Wednesday, February 13, 2013 at 3:08pm
maximum product occurs when a=b=50
That makes the product 2500
The larger a gets, the smaller b must get, so try
a=40 b=60: ab=2400
a=30 b=70: ab=2100
a=20 b=80: ab=1600
and narrow in on it.
Or, algebraically,
a(100a) >= 2000
a^2  100a + 2000 <= 0
10(5√5) <= a <= 10(5+√5)
27.6 <= a <= 72.3
so, 28 < a <= 72
check:
28*72 = 2016
27*73 = 1971
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