How many pairs of positive integers (x,y) satisfy the equation x^0.5-17^0.5=y^0.5
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How many pairs of positive integers (x,y) satisfy the equation x^0.5-17^0.5=y^0.5

[From: ] [author: ] [Date: 11-08-27] [Hit: ]
17^3, 17^5, etc. and their applicable recipricals.There are infinitely many solutions.Answer E.......
(those are square roots btw ^)

A) 0
B) 1
C) 2
D) 17
E) infinitely many

-
sqrt(y) = sqrt(x) - sqrt(17)
y = [ sqrt(x) - sqrt(17) ]^2
y = x - 2sqrt(17x) + 17
For any given x, where x>=0, there is a y value; mind you, for most integer for x will give an irrational y, except for 0, 17, 17^3, 17^5, etc. and their applicable recipricals. There are infinitely many solutions.

Answer E.
1
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