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Question Number 85198 by otchereabdullai@gmail.com last updated on 19/Mar/20

$$\mathrm{Find}\mathrm{x}\mathrm{if}{}^3\sqrt{\mathrm{x}}+\sqrt{\mathrm{x}}=\sqrt{12}$$

Answered by MJS last updated on 19/Mar/20

$$\mathrm{let}x=y^6$$$$y^3+y^2-\sqrt{12}=0$$$$\mathrm{let}y=z-\frac{1}{3}$$$$z^3-\frac{1}{3}z+\frac{2}{27}-2\sqrt{3}=0$$$$D=4{(-\frac{1}{3})}^3+27{(\frac{2}{27}-2\sqrt{3})}^2>0\Rightarrow$$$$\Rightarrow \mathrm{if}\mathrm{you}\mathrm{need}\mathrm{an}\mathrm{exact}\mathrm{solution}\mathrm{use}$$$${\mathrm{Cardano}}^{\prime }\mathrm{s}\mathrm{formula}$$$$z\approx 1.57613$$$$y\approx 1.24280$$$$x\approx 3.68470$$$$\mathrm{is}\mathrm{the}\mathrm{only}\mathrm{solution}\in \mathbb{C}$$

Commented by otchereabdullai@gmail.com last updated on 19/Mar/20

$$\mathrm{Thanks}\mathrm{a}\mathrm{lot}\mathrm{prof}\mathrm{MJS}\mathrm{you}\mathrm{are}\mathrm{funtastic}$$$$\mathrm{God}\mathrm{bless}\mathrm{you}$$

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