What are the solutions to the equation x^{2015}=x^{2016} ?

The solutions to the equation x^{2015}=x^{2016} are x=0,x=1

Find the zeros of x^{2015}=x^{2016}

The zeros of x^{2015}=x^{2016} are x=0,x=1

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x^{2015} = x^{2016}

x = 0, x = 1

Solution steps

x^{2015} = x^{2016}

Switch sides

x^{2016} = x^{2015}

Move

x^{2015}

to the left side

x^{2016} - x^{2015} = 0

Factor

x^{2016} - x^{2015} : x^{2015} (x - 1)

x^{2015} (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = 1

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

2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 = 0

2 x^{3} = 48

x (2 x + 3) (4 x^{2} - 81) = 0

x^{9} = 2

What are the solutions to the equation x^{2015}=x^{2016} ?
The solutions to the equation x^{2015}=x^{2016} are x=0,x=1
Find the zeros of x^{2015}=x^{2016}
The zeros of x^{2015}=x^{2016} are x=0,x=1