Prove the following propositions If n is an integer and a so

Prove the following propositions. If n is an integer and a solution to n^2 = n + 4, then n > 7. If n is an integer and a solution to n^2 = n + 4, then n

Solution

a) Given, n² = n +4

n² -n - 4 = 0

n = (1+ undert 1 + 16) / 2 or (1- undert 1 + 16) / 2

= (1 + undert17)/2 or (1 - undert17)/2

hence no integer can satisfy n² = n+4

b) False

c)N₁² + N₂² + N₃² = N

N belongs {9,14}, which is not possible

hence this proposition is also false

as N = 10 can not be a sum of three natural numbers