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x = 3

Step-by-step explanation:

given:

f(x) = g(x)

f(x) = x³ - 3x² + 2

g(x) = x² - 6x + 11

find: the value of x

solution:

as given f(x) = g(x) equate each side x³ - 3x² + 2 =  x² - 6x + 11 combine similar terms and equate to zero: x³ - 4x² + 6x - 9 = 0 solve by factoring: (x - 3) (x² - x + 3) use the Zero factor principle: x - 3 = 0 x = 3 for x² - x + 3 = 0 this is a complex solution.

therefore, the value of x = 3