What are the solutions to the equation x^{15}=x^2 ?

The solutions to the equation x^{15}=x^2 are x=0,x=1

Find the zeros of x^{15}=x^2

The zeros of x^{15}=x^2 are x=0,x=1

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x^{15} = x^{2}

x = 0, x = 1

Solution steps

x^{15} = x^{2}

Move

x^{2}

to the left side

x^{15} - x^{2} = 0

Factor

x^{15} - x^{2} : x^{2} (x - 1) (x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1)

x^{2} (x - 1) (x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0 :

No Solution for

x \in R

The solutions are

x = 0, x = 1

(22 - 15)^{5} = (2 x - 15)^{3}

216 x^{6} - 793 x + 216 = 0

8 x^{3} - 84 x^{2} + 262 x - 231 = 0

z^{3} = - 8

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

What are the solutions to the equation x^{15}=x^2 ?
The solutions to the equation x^{15}=x^2 are x=0,x=1
Find the zeros of x^{15}=x^2
The zeros of x^{15}=x^2 are x=0,x=1