Solve for x x^6-8x^3-9=0

Problem

x6−8*x3−9=0

Solution

1. Substitute a new variable to transform the equation into a quadratic form. Let u=x3

2. Rewrite the equation in terms of u

u2−8*u−9=0

3. Factor the quadratic equation by finding two numbers that multiply to −9 and add to −8

(u−9)*(u+1)=0

4. Solve for u by setting each factor to zero.

u=9

u=−1

5. Back-substitute x3 for u to find the values of x

x3=9

x3=−1

6. Calculate the real cube roots for each equation.

x=√(3,9)

x=√(3,−1)

7. Simplify the results.

x=√(3,9)

x=−1

Final Answer

x=√(3,9),−1

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