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Question Number 142653 by Gbenga last updated on 03/Jun/21

$$x^3.e^x=216$$

Answered by MJS_new last updated on 03/Jun/21

$$\mathrm{you}\mathrm{can}\mathrm{only}\mathrm{approximate}$$$$x\approx 2.55781651$$

Commented by mr W last updated on 03/Jun/21

$$x=3\mathbb{W}\left(2\right)\approx 3\times 0.8526055=2.5578165$$

Answered by mr W last updated on 04/Jun/21

$${\left(x^3{e}^x\right)}^{\frac{1}{3}}={216}^{\frac{1}{3}}$$$${xe}^{\frac{x}{3}}=6$$$$\frac{x}{3}{e}^{\frac{x}{3}}=\frac{6}{3}=2$$$$\frac{x}{3}=\mathbb{W}\left(2\right)$$$$\Rightarrow x=3\mathbb{W}\left(2\right)\approx 3\times 0.8526055=2.5578165$$

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