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Find all values of x such that $\sqrt{4x^2} - \sqrt{x^2} = 8$.

 Apr 4, 2021
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+1

 

The square roots are a cinch, but the complication they introduce is that square roots are "plus or minus"  

 

You have (+2x) – (+x) = 8     which is the same as +2x +x = 8    So you have four possibilities, namely:  

 

+2x + x = 8       so  +3x = 8   and x = +8/3

 

+2x – x = 8       so  +x   = 8   and x = +8  

 

–2x + x = 8       so  –x   = 8   and x = –8  

 

–2x – x = 8       so  –3x = 8   and x = –8/3  

 

"all values" are  +8  and  –8  and  +8/3  and  –8/3  

.

 Apr 4, 2021

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