Verified answer

x*3^(x - 1) + 3*3^√(3 - x) = 3^x + x*3^√(3 - x)

одз 3 - x >= 0   x<=3

x*3^(x - 1) + 3*3^√(3 - x) = 3^3^(x-1) + x*3^√(3 - x)

x*3^(x - 1) - 3^3^(x-1)=  x*3^√(3 - x) - 3*3^√(3 - x)

3^(x - 1)(x - 3) =  3^√(3 - x)(x - 3)

3^(x - 1)(x - 3) -  3^√(3 - x)(x - 3) = 0

(x - 3)(3^(x - 1) -  3^√(3 - x)) = 0

1. x = 3

2. 3^(x - 1) =  3^√(3 - x)

(x - 1) =  √(3 - x)

(x - 1)² =  (3 - x)

x² - 2x + 1 = 3 - x

x² -x -2 = 0

D = 1 + 8 = 3

x12 = (1 +- 3)/2 = -1   2

ответ -1,2,3