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Question Number 208412 by efronzo1 last updated on 15/Jun/24

Answered by A5T last updated on 15/Jun/24

$$8={24}^{\frac{1}{a}},27={24}^{\frac{1}{b}},64={24}^{\frac{1}{c}}$$$$\Rightarrow {24}^3=8\times 27\times 64={24}^{(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{ab+bc+ca}{abc})}$$$$\Rightarrow \frac{ab+bc+ca}{abc}=3\Rightarrow \frac{2022abc}{ab+bc+ca}=2022\times \frac{1}{3}=674$$

Answered by MM42 last updated on 15/Jun/24

$$a=\frac{1}{3{log}_{2}24}\mathrm{\&}b=\frac{1}{3{log}_{3}24}\mathrm{\&}c=\frac{1}{3{log}_{4}24}$$$$A=\frac{2022}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}=\frac{2022}{3({log}_{2}24+{log}_{3}24+{log}_{4}24)}$$$$=\frac{2022}{3}=674✓$$

Commented by efronzo1 last updated on 15/Jun/24

$$674$$

Commented by MM42 last updated on 15/Jun/24

$$\underset{―}{\underbrace{⋚}}$$

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