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Substituting $x + y + z = 1$, we get:
For positive real numbers with fixed sum, the sum $xy + yz + zx$ is maximized when $x = y = z$. Given $x + y + z = 1$, this occurs when $x = y = z =
We now verify that this is indeed the minimum. Note that for any positive $x, y, z$ with $x + y + z = 1$,
Question: Let $g(x)$ be a polynomial such that
Substitute $a = -2$, $b = 14$ into (1):
h(4) = -2(16) + 14(4) = -32 + 56 = 24
Question: A cartographer is aligning a coordinate transformation used in high-resolution satellite mapping. If
Solution: We are given a recurrence-type functional equation:
This suggests $f(x)$ is a quadratic function, since the first difference is linear in $x$.
Question: Let $a$ and $b$ be real numbers such that