(Geometric and arithmetic mean)How to prove the function $G(x)-\alpha A(x)$ is concave?

Question

The geometric and arithmetic means of $x\in R^n_+$ are, respectively, $$G(x)=(\prod^n_{i=1}x_i)^{1/n},\quad A(x)=\frac{1}{n}\sum^n_{i=1}x_i$$ Suppose $0\leq \alpha\leq 1$, how to prove the function $G(x)-\alpha A(x)$ is concave? I try to solve it by Hessian matrix, but it seems not work.