Solve for x x^6-6x^3+9=0

Problem

x^6−6*x^3+9=0

Solution

1. Identify the equation as a quadratic in form by noticing that x^6 is the square of x^3

2. Substitute a new variable u=x^3 to rewrite the equation.

u^2−6*u+9=0

3. Factor the quadratic expression, which is a perfect square trinomial.

(u−3)^2=0

4. Solve for u by taking the square root of both sides.

u−3=0

u=3

5. Substitute back x^3 for u to solve for x

x^3=3

6. Apply the cube root to both sides to isolate x

x=√(3,3)

Final Answer

x=√(3,3)

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