Algebra
# Geometric Inequalities

$\large \sqrt{a^2+1}+\sqrt{b^2+16}+\sqrt{c^2+49}$

For $a,b,c \in \mathbb R$ such that $a+b+c=5$, what is the minimum value of the expression above?

Given constants $\lambda ,\mu \in { \Re }^{ + }$, consider the set of points $x, y$ such that $2 \leq \left| x+y+\lambda \right| + \left| x-y+\mu \right| \leq 4.$

What is the area of this region ?

$\large \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1}$

If the maximum value of the function above can be expressed as $\sqrt{a}$ , find the value of $a^2$.