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Question Number 115695 by ZiYangLee last updated on 27/Sep/20

$$\mathrm{The}\mathrm{product}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{solutions}\mathrm{of}\mathrm{the}$$$$\mathrm{equation}\mid {(x-2)}^2\mid -3\mid x-2\mid +2=0\mathrm{is}$$

Answered by MJS_new last updated on 27/Sep/20

$$x=0\mathrm{is}\mathrm{a}\mathrm{solution}\Rightarrow \mathrm{answer}\mathrm{is}0$$

Answered by mathmax by abdo last updated on 27/Sep/20

$$\mathrm{e}\Rightarrow {\mathrm{u}}^2-3\mathrm{u}+2=0\mathrm{with}\mathrm{u}=\mid \mathrm{x}-2\mid (\mathrm{so}\mathrm{u}⩾0)$$$$\mathrm{\Delta }=9-8=1\Rightarrow {\mathrm{u}}_1=\frac{3+1}{2}=2\mathrm{and}{\mathrm{u}}_2=\frac{3-1}{2}=1$$$$\mid \mathrm{x}-2\mid =2\Rightarrow \mathrm{x}-2=2\mathrm{or}\mathrm{x}-2=-2\Rightarrow \mathrm{x}=4\mathrm{or}\mathrm{x}=0$$$$\mid \mathrm{x}-2\mid =1\Rightarrow \mathrm{x}-2=1\mathrm{or}\mathrm{x}-2=-1\Rightarrow \mathrm{x}=3\mathrm{or}\mathrm{x}=1$$$$\Rightarrow \mathrm{\Pi }\left(\mathrm{of}\mathrm{roots}\right)=0$$

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