What are the solutions to the equation x^9+x^6-36=0 ?

The solutions to the equation x^9+x^6-36=0 are

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x^9+x^6-36=0

x^{9} + x^{6} - 36 = 0

Solution steps

x^{9} + x^{6} - 36 = 0

Rewrite the equation with

u = x^{3}, u^{2} = x^{6}

and

u^{3} = x^{9}

u^{3} + u^{2} - 36 = 0

Solve

u^{3} + u^{2} - 36 = 0 : u = 3, u = - 2 + 22 i, u = - 2 - 22 i

u = 3, u = - 2 + 22 i, u = - 2 - 22 i

Substitute back

u = x^{3},

solve for

x

Solve

The solutions are

- 4500 x^{3} - 1950 x^{2} - 205 x - 3 = 0

(x^{2} + 2 x)^{2} - 2 (x^{2} + 2 x) - 3 = 0

x, 9 x^{6} - 7 x^{2} = 0

4 x^{3} - 15 x^{2} + 12 x = 0

x^{3} + 3 x^{2} - x - 3

What are the solutions to the equation x^9+x^6-36=0 ?
The solutions to the equation x^9+x^6-36=0 are
Find the zeros of x^9+x^6-36=0
The zeros of x^9+x^6-36=0 are