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Question Number 10043 by konen last updated on 21/Jan/17

$$\mid \mathrm{x}-3{\mid }^{{\mathrm{x}}^2-9}=1\Rightarrow \mathrm{\Sigma }\mathrm{x}=?$$

Answered by mrW1 last updated on 22/Jan/17

$$if{a}^b=1,then$$$$a=1or$$$$b=0anda\ne 0$$$$$$$$since\mid \mathrm{x}-3{\mid }^{{\mathrm{x}}^2-9}=1$$$$\Rightarrow \mid x-3\mid =1...\left(i\right)$$$$\Rightarrow x^2-9=0andx-3\ne 0...\left(ii\right)$$$$$$$$from\left(i\right)\Rightarrow$$$$x-3=\pm 1$$$$x=\pm 1+3$$$$\Rightarrow x=2or4$$$$$$$$from\left(ii\right)\Rightarrow$$$$x^2=9andx\ne 3$$$$\Rightarrow x=-3$$$$$$$$x=(-3,2,4)$$$$\mathrm{\Sigma }x=-3+2+4=3$$

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