Home / Thus, the number of interior lattice points is $ \boxed{10} $.Question: Compute the sum of the roots of the equation

Thus, the number of interior lattice points is $ \boxed{10} $.Question: Compute the sum of the roots of the equation

February 22, 2026

$Thus, the number of interior lattice points is $ \boxed{10} $.Question: Compute the sum of the roots of the equation$

For $n = 6$:
I = \frac{(6-1)(6-2)}{2} = \frac{5 \cdot 4}{2} = 10
This formula arises from known results in triangular lattice geometry: the number of interior points in a triangle of side $n$ is $\frac{n(n-2)(n-1)}{6}$, or equivalently $\frac{(n-1)(n-2)}{2}$.
u\sqrt{u} - 5u + 6\sqrt{u} = 0,
given that all of the roots are real and nonnegative.
Solution: Let us make the substitution $ x = \sqrt{u} $, so that $ u = x^2 $. Substituting into the equation gives: