Solving A Trigonometric Exponential Equation

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[@quantumbuddha777]

Fun problem! Thanks! I generalized the solution to (3k+/-1)pi/6,k€Z

[@saidtakadda6799]

Hello,
i use the same method , i think the solutions are:
Pi/6 + k*Pi , -Pi/6 + k*Pi , Pi/3 + k*Pi , -Pi/3 + k*Pi where k belong to Z

[@hrvojedjurdjevic2123]

You are right.

[@phill3986]

More steps is better, just watch at 2x

[@SidneiMV]

4^sin²x = u
u + 4/u = 3√2
u² - (3√2)u + 4 = 0
u = (3√2 ± √2)/2
u = 2√2 or u = √2
u = 2√2
4^sin²x = 2√2 = 2^(3/2)
2sin²x = 3/2 => sin²x = 3/4
sinx = ± (√3)/2
u = √2
4^sin²x = √2 = 2^(1/2)
2sin²x = 1/2 => sin²x = 1/4
sinx = ± 1/2
*x = kπ/6 (except for k = 3n)*

[@pablocopello3592]

+-Pi/6 + k*Pi/2; k integer.
OR
+-(Pi/6 + n*Pi/2); n natural

[@nizamkanchon3311]

Could u please kindly give me the pdf of aops introduction to algebra solutions manual?
Anyway, ur work has been a great help. Please keep it up

[@scottleung9587]

Got 'em all!

[@phill3986]

😊🎉😊👍😊, degrees vs radians ouch!

[@padraiggluck2980]

I suggest you graph in Desmos.

[@SyberMath]

Sometimes you need to zoom out or zoom in to see what’s going on with desmos

[@padraiggluck2980]

@@SyberMath The left side lies in [4,5] for all x and is disjoint from y = sqrt(3)/2

[@yakupbuyankara5903]

X=60degrees