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The product of sum and difference of two numbers is 1995. There are eight groups of natural numbers satisfying this condition. Which group of natural numbers has the most difference among the eight groups
Let two numbers be x, y and x > y
(x-y)(x+y)=1995
The difference between the two natural numbers should be the largest, that is, X-Y should be as large as possible
1995=3×5×7×19
x-y= 1,3,5,7,15,19,21,35
x+y=1955,665,399,285,133,105,95,57
So X-Y = 35, x + y = 57
So x = 46, y = 11
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