What are the solutions to the equation (x^3-1)(x^5-1)=0 ?

The solutions to the equation (x^3-1)(x^5-1)=0 are x=1

Find the zeros of (x^3-1)(x^5-1)=0

The zeros of (x^3-1)(x^5-1)=0 are x=1

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(x^{3} - 1) (x^{5} - 1) = 0

x = 1

Solution steps

(x^{3} - 1) (x^{5} - 1) = 0

Factor

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

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 1 = 0 :

No Solution for

x \in R

Solve

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

No Solution for

x \in R

The solution is

x = 1

\frac{2 x ^{4} - 1}{8} = 0

y^{3} - 3 = 1

(x^{2} + 4)^{2} - 13 (x^{2} + 4) + 40 = 0

125 x^{4} + x = 0

x^{3} - 7 x + 3 = 0

What are the solutions to the equation (x^3-1)(x^5-1)=0 ?
The solutions to the equation (x^3-1)(x^5-1)=0 are x=1
Find the zeros of (x^3-1)(x^5-1)=0
The zeros of (x^3-1)(x^5-1)=0 are x=1