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Question Number 154493 by mathdanisur last updated on 18/Sep/21

$$\mathrm{If}\mathrm{a};\mathrm{b};\mathrm{c}>0\mathrm{and}\mathrm{n}\in {\mathbb{N}}^{+}\mathrm{then}:$$ $$\frac{{\mathrm{a}}^{2\mathbf{n}}+{\mathrm{b}}^{2\mathbf{n}}+{\mathrm{c}}^{2\mathbf{n}}}{{\mathrm{a}}^{\mathbf{n}}{\mathrm{b}}^{\mathbf{n}}+{\mathrm{b}}^{\mathbf{n}}{\mathrm{c}}^{\mathbf{n}}+{\mathrm{c}}^{\mathbf{n}}{\mathrm{a}}^{\mathbf{n}}}⩾\frac{\sqrt{3\cdot ({\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2)}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}$$

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