Question 252536: How many different values of n are there such that n is a natural number and
n^2 - 20 is a perfect square?
(a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How many different values of n are there such that n is a natural number and
n^2 - 20 is a perfect square?
(a) 1 (b) 2 (c) 3 (d) 4 (e) infinitely many
There are 2, +6 and -6.
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a^2 - b^2 = 20
(a-b)*(a+b) = 20
This is one eqn in two variables, but restricted to integers.
20 = 1*20, 2*10 or 4*5
1 and 20
a-b = 1
a+b = 20 Not integers
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2 and 10
a-b = 2
a+b = 10
--> 4 and 6 which works
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4 and 5 no integer solution
6^2 - 20 = 4^2
(-6)^2 - 20 = 4^2
No other solutions.
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