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Question Number 74611 by chess1 last updated on 27/Nov/19

Answered by mind is power last updated on 27/Nov/19

$$\mathrm{et}\mathrm{x}=\mathrm{a}+1,\mathrm{y}=\mathrm{b}+1,\mathrm{z}=\mathrm{c}+1$$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=11$$$$\frac{81}{\mathrm{x}.\mathrm{y}.\mathrm{z}}⩾\frac{1}{\sqrt[4]{27}}$$$$\iff \mathrm{xyz}⩽81.\sqrt[4]{27}$$$$\mathrm{AM}-\mathrm{GM}\Rightarrow \mathrm{xyz}⩽{\left(\frac{\mathrm{x}+\mathrm{y}+\mathrm{z}}{3}\right)}^3$$$$\mathrm{xyz}⩽{\left(\frac{\mathrm{x}+\mathrm{y}+\mathrm{z}}{3}\right)}^3=\frac{{11}^3}{27}⩽81.\sqrt[4]{27}$$$${11}^3=121.11=1331$$$$81.27⩾1600\mathrm{cause}$$

Commented by chess1 last updated on 27/Nov/19

$$\mathrm{thanks}$$

Commented by mind is power last updated on 27/Nov/19

$${\mathrm{y}}^{\prime }\mathrm{re}\mathrm{welcom}$$

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