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Question Number 156359 by MathSh last updated on 10/Oct/21

$$\mathrm{if}\mathrm{a};\mathrm{b};\mathrm{c}>0\mathrm{and}\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=3$$ $$\mathrm{then}\mathrm{prove}\mathrm{that}:$$ $$\sqrt[3]{({\mathrm{a}}^3+1)({\mathrm{b}}^3+1)({\mathrm{c}}^3+1)}⩾2$$

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