Linear Algebra Done Right · Problem 6A.8

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products-and-norms

Problem

Suppose

a, b, c, x, y \in \mathbf{R}

and

a^2 + b^2 + c^2 + x^2 + y^2 \leq 1

. Prove that

a + b + c + 4x + 9y \leq 10.