Let $\lambda$ be a positive real number. Inequality $|\lambda xy+yz|\le \dfrac{\sqrt5}{2}$ holds for arbitrary real numbers $x, y, z$ satisfying $x^2+y^2+z^2=1$. Find the maximal value of $\lambda$.
Problem
Source: China south east mathematical Olympiad 2008 day2 problem 5
Tags: inequalities, inequalities unsolved