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

#1

#2**0 **

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**+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 x_{1}, but LHS = RHS only for odd values of m for x_{2}.

(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