We have the constraint x squared plus y squared equals 5, and we want to find the minimum value of x plus 2y using the Cauchy-Schwarz inequality. We can visualize this as a circle of radius square root of 5 in the coordinate plane. The Cauchy-Schwarz inequality states that for vectors (x, y) and (1, 2), the dot product squared is less than or equal to the product of their squared magnitudes.