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Question Number 205422 by hardmath last updated on 20/Mar/24

$$\mathrm{If}$$$$(\mathrm{a}+1)(\mathrm{b}+1)(\mathrm{c}+1)=8$$$$\mathrm{Then}:$$$${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2⩾3$$

Answered by A5T last updated on 20/Mar/24

$$a+1+b+1+c+1⩾3\sqrt[3]{(a+1)(b+1)(c+1)}=6$$$$\Rightarrow a+b+c⩾3$$$$\sqrt{3}\sqrt{a^2+b^2+c^2}⩾a+b+c\Rightarrow a^2+b^2+c^2⩾3$$

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