What are the solutions to the equation x^{12}-1=4 ?

The solutions to the equation x^{12}-1=4 are

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x^{12}-1=4

x^{12} - 1 = 4

Solution steps

x^{12} - 1 = 4

Move

1

to the right side

x^{12} = 5

Rewrite the equation with

u = x^{2}

and

u^{6} = x^{12}

u^{6} = 5

Solve

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 0.65383 \dots + 1.13246 \dots i : x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

Solve

x^{2} = - 0.65383 \dots - 1.13246 \dots i : x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

Solve

x^{2} = - 0.65383 \dots + 1.13246 \dots i : x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

Solve

x^{2} = 0.65383 \dots - 1.13246 \dots i : x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

The solutions are

7 x^{3} - 9 x^{2} - 7 x = - 9

7 π k^{3} = 22704

x = x^{3} - 2 x^{2} + 1

x^{3} - 2 x^{2} + x - 1 = - x^{2} + 3 x - 1

30 x^{4} - 30 x^{2} = 0

What are the solutions to the equation x^{12}-1=4 ?
The solutions to the equation x^{12}-1=4 are
Find the zeros of x^{12}-1=4
The zeros of x^{12}-1=4 are