SOLUTION: 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

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.
------------------------
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
------------------------
2 and 10
a-b = 2
a+b = 10
--> 4 and 6 which works
------------------------
4 and 5 no integer solution
6^2 - 20 = 4^2
(-6)^2 - 20 = 4^2
No other solutions.
RELATED QUESTIONS
1) A warehouse contains 200 shoes of size 8, 200 shoes of size 9 and 200 shoes of size... (answered by psbhowmick)

if n>1 and each of the three integers n, n+2,and n+4 is a prime number, then the set of... (answered by stanbon)

Find the smallest number, n, such that n/2 is a perfect square and n/3 is a perfect... (answered by user_dude2008)

find a natural number n, such that 2^8 + 2^10 + 2^n is a perfect square... (answered by CubeyThePenguin)

1) There exists a 5 digit number N with distinct and non-zero digits such that it equals... (answered by Edwin McCravy)

Prove that there exists some integer n such that n^2 + 123457 is a perfect... (answered by Edwin McCravy)

16. Find the value of n such that x2 + 2x + n is a perfect square trinomial. 4 �1 (answered by Theo)

16. Find the value of n such that x2 + 2x + n is a perfect square trinomial. 4 �1 (answered by rapaljer)

Find the value of n suck that x^2-17x+n is a perfect square trinominal. a. 289/2 b.... (answered by Fombitz)