Question 273266
from all the pairs of numbers whose sum is 256, find the pair whose product is greatest.

pair of numbers: a and b

a + b = 256

a * b greatest = ?

this will be when a and b are both greatest or a=128 and b=128,
then a*b = 128 * 128 = 16384

this is similar to when you have a set perimeter for a rectangle, a square will always have the greatest area

following table is proof:
a	b	a*b
0	256	0
1	255	255
2	254	508
...
125	131	16375
126	130	16380
127	129	16383
128	128	16384
129	127	16383
130	126	16380
131	125	16375
132	124	16368
133	123	16359
134	122	16348
135	121	16335
...
254	2	508
255	1	255
256	0	0