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How you solve this? Solve in #ZZ_6# equation:#hat(x)^3=hatx#

Answer 1

Eli Assouline

All elements of #ZZ_6# satisfy #x^3 = x#

Modulo #6# we find:

#0^3 = 0#

#1^3 = 1#

#2^3 = 8 -= 2#

#3^3 = 27 -= 3#

#4^3 = 64 -= 4#

#5^3 = 125 -= 5#

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Answer 2

Avery Alexander

To solve the equation (\hat{x}^3 = \hat{x}) in ( \mathbb{Z}_6 ), we find the solutions by testing each element of ( \mathbb{Z}_6 ) for ( \hat{x} ), which are ( \hat{x} = {0, 1, 2, 3, 4, 5} ). Upon testing, we find that the solutions are ( \hat{x} = {0, 1, 5} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.