Algebra
# Completing The Square

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

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

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

\[ (2x-3y-4)^2 + (2x-3y+10)^2 ?\]

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

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