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Question Number 201689 by cherokeesay last updated on 10/Dec/23

Answered by witcher3 last updated on 10/Dec/23

$${\mathrm{x}}^3-{6\mathrm{x}}^2+12\mathrm{x}-32={(\mathrm{x}-2)}^3-24$$$$\mathrm{x}-2=\mathrm{y}$$$$\iff \sqrt[3]{\mathrm{y}+24}={\mathrm{y}}^3-24$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}+24}\Rightarrow {\mathrm{f}}^{-}\left(\mathrm{y}\right)={\mathrm{y}}^3-24$$$$\mathrm{conclusion}\mathrm{withe}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{f}}^{-}\left(\mathrm{x}\right)\Rightarrow \mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}$$$${\mathrm{y}}^3-24-\mathrm{y}=0\Rightarrow (\mathrm{y}-3)({\mathrm{x}}^2+3\mathrm{x}+8)=0$$$$\mathrm{y}=3;\Rightarrow \mathrm{x}=5$$$$$$

Commented by cherokeesay last updated on 10/Dec/23

$$Nice!thankyou!$$

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