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Question Number 55756 by otchereabdullai@gmail.com last updated on 03/Mar/19

$$\mathrm{Find}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{real}\mathrm{values}$$$$\mathrm{of}\mathrm{a}\mathrm{that}\mathrm{satisfies}\mathrm{the}\mathrm{equation}$$$$4\mid \mathrm{a}-4\mid =\mid \mathrm{a}+4\mid$$

Answered by mr W last updated on 03/Mar/19

$$ifa⩽-4:$$$$-4(a-4)=-(a+4)$$$$\Rightarrow a=\frac{20}{3}>0\Rightarrow nosolution$$$$$$$$if-4<a⩽4$$$$-4(a-4)=a+4$$$$\Rightarrow a=\frac{12}{5}=2.4\Rightarrow solution$$$$$$$$if4<a:$$$$4(a-4)=a+4$$$$\Rightarrow a=\frac{20}{3}=6.67\Rightarrow solution$$$$$$$$allsolutionsare:$$$$a=\frac{12}{5}and\frac{20}{3}$$$$\Rightarrow \frac{12}{5}\times \frac{20}{3}=16$$

Commented by otchereabdullai@gmail.com last updated on 03/Mar/19

$$\mathrm{Thank}\mathrm{you}\mathrm{soo}\mathrm{much}\mathrm{Prof}\mathrm{W}$$

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