Showing posts with label Lagrange multipliers method. Show all posts
Showing posts with label Lagrange multipliers method. Show all posts

Friday, June 5, 2015

Third Method of Solving IMO Optimization Contest Problem: Find the minimum value of $xy$,

Third Method of Solving IMO Optimization Contest Problem:

Find the minimum value of $xy$, given that $x^2+y^2+z^2=7$, $xy+xz+yz=4$, and $x, y$ and $z$ are real numbers.

This third method is provided by Mark, another blog contributor and he approached the problem using the well-known Lagrange multipliers method: