SOLUTION: when 2^X - 2^(-x) = 4, then 2^(2x) + 2^(-2x) = ... , and 2^(3x) - 2^(-3X) = ...

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Question 1069225: when 2^X - 2^(-x) = 4, then 2^(2x) + 2^(-2x) = ... , and 2^(3x) - 2^(-3X) = ...
Answer by ikleyn(52914) About Me  (Show Source):
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When 2^X - 2^(-x) = 4, then 2^(2x) + 2^(-2x) = ... , and 2^(3x) - 2^(-3X) = ...
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1. 
    When 2^X - 2^(-x) = 4,    (1)

    then  (squaring both sides of (1) )   2%5E%282x%29+-+2+%2B+2%5E%28-2x%29 = 4%5E2 = 16,

    then                                  2%5E%282x%29+%2B+2%5E%28-2x%29 = 16 + 2 = 18.


    Answer.   when 2^X - 2^(-x) = 4, then  2%5E%282x%29+%2B+2%5E%28-2x%29 = 18.


For #2, follow the same scheme/idea, but instead of squaring, raise in degree 3 both sides.