What are the solutions to the equation x^5=9x ?

The solutions to the equation x^5=9x are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)

Find the zeros of x^5=9x

The zeros of x^5=9x are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)

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x^{5} = 9 x

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

Solution steps

x^{5} = 9 x

Move

9 x

to the left side

x^{5} - 9 x = 0

Factor

x^{5} - 9 x : x (x^{2} + 3) (x + 3) (x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} + 3 = 0 or x + 3 = 0 or x - 3 = 0

Solve

x^{2} + 3 = 0 : x = 3 i, x = - 3 i

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

5 x^{4} = 135 x

6 n^{4} + 9 n^{3} + 3 n^{2} = 0

x^{5} = 16

- x^{3} - 4 x^{2} + 16 x + 64 = 0

x^{3} + 6 x^{2} + 9 x + 9 = 0

What are the solutions to the equation x^5=9x ?
The solutions to the equation x^5=9x are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)
Find the zeros of x^5=9x
The zeros of x^5=9x are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)