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July 24th, 2018, 01:23 AM   #1
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One exponential equation

Equation
81^\sin^2 x+81^\cos^2 x=30
can easy be solved by substitution 81^\sin^2 x=t
What about equation
81^\sin2x+81^\cos2x=30?
I think it doesn't have real solutions.

Last edited by skipjack; July 24th, 2018 at 01:50 AM.
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July 24th, 2018, 01:52 AM   #2
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It seems to have real solutions. Why do you think it doesn't?
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July 24th, 2018, 02:59 AM   #3
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Math Focus: Wibbly wobbly timey-wimey stuff.
See here.

I can't think of a way to solve it in closed form if that's what you mean.

-Dan

Last edited by topsquark; July 24th, 2018 at 03:02 AM.
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