What are the solutions to the equation x^9-x^5+x^4-1=0 ?

The solutions to the equation x^9-x^5+x^4-1=0 are x=-1,x=1

Find the zeros of x^9-x^5+x^4-1=0

The zeros of x^9-x^5+x^4-1=0 are x=-1,x=1

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x^{9} - x^{5} + x^{4} - 1 = 0

x = - 1, x = 1

Solution steps

x^{9} - x^{5} + x^{4} - 1 = 0

Factor

x^{9} - x^{5} + x^{4} - 1 : (x^{2} + 1) (x + 1)^{2} (x - 1) (x^{4} - x^{3} + x^{2} - x + 1)

(x^{2} + 1) (x + 1)^{2} (x - 1) (x^{4} - x^{3} + x^{2} - x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{2} + 1 = 0 or x + 1 = 0 or x - 1 = 0 or x^{4} - x^{3} + x^{2} - x + 1 = 0

Solve

x^{2} + 1 = 0 :

No Solution for

x \in R

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

Solve

x^{4} - x^{3} + x^{2} - x + 1 = 0 :

No Solution for

x \in R

The solutions are

x = - 1, x = 1

(\frac{x - 1}{3})^{3} = \frac{8}{25}

x^{50} = 1

x^{4} - 2 x^{3} - 4 x + 5 = 0

\frac{x ^{4}}{3} = 16

\frac{5}{2} x + 1 - 2 \frac{x}{1} - 2 x = 1 - 2 \frac{( 3 - 2 x )}{4} x^{2} - 1

What are the solutions to the equation x^9-x^5+x^4-1=0 ?
The solutions to the equation x^9-x^5+x^4-1=0 are x=-1,x=1
Find the zeros of x^9-x^5+x^4-1=0
The zeros of x^9-x^5+x^4-1=0 are x=-1,x=1