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(3-2*sqrt(2))^x+(3+2*sqrt(2))^x=6 equation

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The solution

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             x                x    
/        ___\    /        ___\     
\3 - 2*\/ 2 /  + \3 + 2*\/ 2 /  = 6
$$\left(3 - 2 \sqrt{2}\right)^{x} + \left(2 \sqrt{2} + 3\right)^{x} = 6$$
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Numerical answer [src]
x1 = 1.0
x2 = -1.0
x2 = -1.0