Question

If x^6 = x^8, name all the possible real number values of x that satisfy this equation. Explain your answer.

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Please explain how you found your answer.

Answer 1

x^6=x^8 subtract x^8 from both sides

x^6-x^8=0 factor out x^6

x^6(1-x^2)=0 now factor parenthetical term

x^6(1-x)(1+x)=0

So the values of x that satisfy the above condition are:

x=-1,0,1