Question 59
Let $m, n, p$ be fixed positive real numbers which satisfy $mnp = 8$. Depending on these constants, find the minimum of
$$
x^2 + y^2 + z^2 + mxy + nxz + pyz
$$
where $x, y, z$ are arbitrary positive real numbers satisfying $xyz = 8$. When is the equality attained?
a) $m = n = p = 2$
b) arbitrary (but fixed) positive real numbers $m, n, p$.
$$
x^2 + y^2 + z^2 + mxy + nxz + pyz
$$
where $x, y, z$ are arbitrary positive real numbers satisfying $xyz = 8$. When is the equality attained?
a) $m = n = p = 2$
b) arbitrary (but fixed) positive real numbers $m, n, p$.