Answer:
Proved
Step-by-step explanation:
To prove that if n is a perfect square, then n+1 can never be a perfect square
Let n be a perfect square
[tex]n=x^2[/tex]
Let [tex]n+1 = y^2[/tex]
Subtract to get
[tex]1 = y^2-x^2 =(y+x)(y-x)[/tex]
Solution is y+x=y-x=1
This gives x=0
So only 0 and 1 are consecutive integers which are perfect squares
No other integer satisfies y+x=y-x=1
