hi, Can any of you help me to give me proof of these inequlities:

(1)

$\displaystyle

(a+b)^{\alpha}\leq 2^{\alpha-1}(a^{\alpha}+b^{\alpha})\quad\text{for }a,b\geq 0 \quad\text{and

}\alpha\geq1

$

and

(2)

$\displaystyle

|x|^{\alpha}\leq1+|x|\quad\text{for } x\in\mathbb{R}\quad\text{and } \alpha\in[0,1].

$

thanx for all,,