Prove $$\min\{a,b\} \le H \le G \le A \le R \le \max\{a,b\}$$ where $$ H=\frac{2ab}{a+b},\quad G=\sqrt{ab},\quad A=\dfrac{a+b}{2},\quad R=\sqrt{\dfrac{a^2+b^2}{2}} $$