Solve for x x^5-6x^2=0

Problem

x^5−6*x^2=0

Solution

1. Identify the common factor in both terms of the equation.

2. Factor out the greatest common factor, which is x^2

x^2*(x^3−6)=0

3. Apply the zero product property by setting each factor equal to zero.

x^2=0

x^3−6=0

4. Solve the first equation for x

x=0

5. Solve the second equation for x by isolating the variable.

x^3=6

6. Take the cube root of both sides to find the real solution.

x=√(3,6)

Final Answer

x=0,√(3,6)

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