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Question Number 178635 by infinityaction last updated on 19/Oct/22

$$\mathrm{solution}\mathrm{set}\mathrm{of}{\log }_{{\mathrm{x}}^2}(\frac{\mathrm{x}}{\mid \mathrm{x}\mid }-\mathrm{x})⩾0$$

Commented by Frix last updated on 19/Oct/22

$$x⩽-2\vee 0<x<1$$

Commented by infinityaction last updated on 20/Oct/22

$$sirsolution$$

Answered by mr W last updated on 20/Oct/22

$$for{x}^2⩾1:\frac{x}{\mid x\mid }-x⩾1$$$$forx>0:$$$$1-x⩾1\Rightarrow x⩽0\Rightarrow contradition!$$$$forx<0:$$$$-1-x⩾1\Rightarrow x⩽-2✓$$$$$$$$for{x}^2⩽1:0<\frac{x}{\mid x\mid }-x⩽1$$$$forx>0:$$$$0<1-x⩽1\Rightarrow x⩾0\Rightarrow 1>x>0✓$$$$forx<0:$$$$0<-1-x⩽1\Rightarrow -2⩽x<-1\Rightarrow contradiction$$$$$$$$\Rightarrow solution:x⩽-2or0<x<1$$

Commented by infinityaction last updated on 21/Oct/22

$$thankyousir$$

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