What are the solutions to the equation x^3=x^7 ?

The solutions to the equation x^3=x^7 are x=0,x=i,x=-i,x=-1,x=1

Find the zeros of x^3=x^7

The zeros of x^3=x^7 are x=0,x=i,x=-i,x=-1,x=1

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x^{3} = x^{7}

x = 0, x = i, x = - i, x = - 1, x = 1

Solution steps

x^{3} = x^{7}

Switch sides

x^{7} = x^{3}

Move

x^{3}

to the left side

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

Factor

x^{7} - x^{3} : x^{3} (x^{2} + 1) (x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} + 1 = 0 : x = i, x = - i

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = i, x = - i, x = - 1, x = 1

m^{3} = \frac{1}{125}

2 x^{4} + 6 x^{3} - 8 x^{2} - 24 x = 0

2 x (x^{3} - 216) = 0

x^{4} + 2 x^{3} - 14 x^{2} + 2 x + 1 = 0

0.5 (5 - 7 x) = 8 - (4 x^{6})

What are the solutions to the equation x^3=x^7 ?
The solutions to the equation x^3=x^7 are x=0,x=i,x=-i,x=-1,x=1
Find the zeros of x^3=x^7
The zeros of x^3=x^7 are x=0,x=i,x=-i,x=-1,x=1