Show the inequality $$\forall (A, B) \in S_n^{++}(\mathrm{R})^2, \quad \operatorname{det}^{1/n}(A + B) \geq \operatorname{det}^{1/n}(A) + \operatorname{det}^{1/n}(B)$$
Show the inequality
$$\forall (A, B) \in S_n^{++}(\mathrm{R})^2, \quad \operatorname{det}^{1/n}(A + B) \geq \operatorname{det}^{1/n}(A) + \operatorname{det}^{1/n}(B)$$