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Question Number 197623 by hardmath last updated on 24/Sep/23

$$\mathrm{x},\mathrm{y}\in \mathbb{N}$$$$162\cdot {\mathrm{x}}^2={\mathrm{y}}^3$$$$\min (\mathrm{x}+\mathrm{y})=?$$

Commented by SANOGO last updated on 25/Sep/23

merci bien monsieur

Answered by Frix last updated on 24/Sep/23

$$162=2\times 3^4$$$$\left(2\times 3^4\right)\times {\left(2\times 3\right)}^2=2^3\times 3^6={\left(2\times 3^2\right)}^3$$$$x=6\wedge y=18$$$$x+y=24$$

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