Final answer:
The real solutions of the equation 27x - x⁴ = 0 are x = 0 and x = 3. This is obtained by factoring out x from the given equation and solving for x in each of the resultant factors.
Step-by-step explanation:
The subject of this question is Mathematics, and it's a High School grade level question. The question asks you to solve the equation 27x - x⁴ = 0. This equation can be solved by factoring, as x is a common factor.
We start by factoring out x: x*(27 - x³) = 0. We set both factors equal to zero and solve independently to find all real solutions. So, we have x = 0 and 27 - x³ = 0.
The equation 27 - x³ = 0 gives x³ = 27. Taking the cubic root of both sides gives x = 3. Therefore, the real solutions of the equation are x = 0 and x = 3.
Learn more about Solving Polynomial Equations