grandes-ecoles 2011 Q2

grandes-ecoles · France · centrale-maths1__pc Proof Direct Proof of an Inequality

Let $a$ and $b$ be two non-negative real numbers and $\lambda$ a real number in $]0,1[$. Show that $$(a+b)^{\lambda} \leq a^{\lambda} + b^{\lambda}$$

Let $a$ and $b$ be two non-negative real numbers and $\lambda$ a real number in $]0,1[$. Show that
$$(a+b)^{\lambda} \leq a^{\lambda} + b^{\lambda}$$