Euclidean metric (L2 norm) versus taxicab metric(L1 norm)

[mglaros]

Homework Statement

I was just wondering how I would go about proving that the euclidean metric is always smaller than or equal to the taxicab metric for a given vector x in R^n. The result seems obvious but I am not sure how I would show this.

Homework Equations

The Attempt at a Solution

 

[D H]

Show that (||x||₁)² - (||x||₂)² can never be negative.