Prove: If n is a perfect square, then n+3 is not a perfect square Use either direct proof, proof by contrapositive, or proof by contradiction.
Using proof by contradiction method

Assume n is a perfect square and n+3 is a perfect square (proof by
contradiction)
There exists integers x and y such that $n = x^2$ and $n+3 = y^2$
Then $x^2 + 3 = y^2$
Then $3 = y^2 - x^2$
Then $3 = (y-x)(y+x)$
Then $y+x = 3$ and $y-x=1$
Then $x = 1, y = 2$
Since $x = 1$, that implies $n = 1$
this is how far I got

Anyone know what I should do now?

$$
3=y^2-x^2 \ge (x+1)^2-x^2= 2x+1
$$
which is false if $x>1$.
