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How do I solve for x the following equation

\(\sqrt[m]{(1+x)^2}-\sqrt[m]{(1-x)^2}=\sqrt[m]{1-x^2}\)

Thanks very much in advance!

sasaki.dnz  Jun 30, 2017
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3+0 Answers

 #1
avatar+26366 
+2

As follows:

 

.

Alan  Jul 1, 2017
 #2
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Thanks for your answer.

 

"However, x_2 is only valid when m is an odd integer."

 

This may be a silly question, but could you explain to me why that is the case? Thanks.

sasaki.dnz  Jul 1, 2017
 #3
avatar+26366 
+1

Easiest way to see this is to look at some numerical examples.  In the matrices below you can see that the LHS = RHS for all values of m for x1, but LHS = RHS only for odd values of m for x2.

 

(The first column of a matrix below is m, the second is the LHS of your original equation, the third is the RHS)

 

Alan  Jul 1, 2017

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