Algebra
# Completing The Square

Find the largest positive integer $x$ such that $\sqrt{ 3620 + 322x - 4x^2 }$ is a real number.

What will be the least value of the expression $\left( x^2+2xy+2y^2+4y+7 \right) ?$

**Note :** $x,y \in \mathbb{R}$

$(x,y)$ ranges over all pairs of real values, what is the smallest value of

As$(2x-3y-4)^2 + (2x-3y+10)^2 ?$

How many positive integral value(s) of $n$ exist such that $n^2+96$ is a perfect square?