Prove $ \\frac{1}{C_{\\alpha}}(x^{\\alpha} + y^{\\alpha}) \\le (x + y)^{\\alpha} \\le C_{\\alpha}(x^{\\alpha} + y^{\\alpha}) $

Prove $ \\frac{1}{C_{\\alpha}}(x^{\\alpha} + y^{\\alpha}) \\le (x + y)^{\\alpha} \\le C_{\\alpha}(x^{\\alpha} + y^{\\alpha}) $ References Suppose that $ 0 < \\alpha < 1 $. Show that there is a constant $ C_{\\alpha} $ so that for $ x, y \\in (0, +\\infty) $ we have the estimate \\begin{equation} \\frac{1}{C_{\\alpha}}(x^{\\alpha} + y^{\\alpha}) \\le (x + y)^{\\alpha} \\le C_{\\alpha}(x^{\\alpha} + y^{\\alpha}) \\end{equation} I tried to divide the expression by $ x^{\\alpha} $ and to use Taylor\'s series, but it didn\'t work out. Can anybody hint what this problem is about?