If two of the four expressions x + y, x + 5y, x - y, and 5x - y are chosen at random, what is the possiblity that their product will be of the form x^2 - (by)^2, where b is an integer?
a) 1/2
b) 1/3
c) 1/4
d) 1/5
e) 1/6
OA: E
I picked B) because to get that form you have to have (x+y) (x-y) format. Since b exists there must be an integer in front of y.
Total of 4 equations pick 2 = 4! / 2!2! = 12/6 = 6 combinations possible
(x+y) x (x - y)
(x + 5y) ( x - y)
Both work, no? Where b is an integer (doesn't 1 couint too?)
2/6 = 1/3
Thanks for your help!
a) 1/2
b) 1/3
c) 1/4
d) 1/5
e) 1/6
OA: E
I picked B) because to get that form you have to have (x+y) (x-y) format. Since b exists there must be an integer in front of y.
Total of 4 equations pick 2 = 4! / 2!2! = 12/6 = 6 combinations possible
(x+y) x (x - y)
(x + 5y) ( x - y)
Both work, no? Where b is an integer (doesn't 1 couint too?)
2/6 = 1/3
Thanks for your help!
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