What are the solutions to the equation x^4-1=0 ?

The solutions to the equation x^4-1=0 are x=1,x=-1,x=i,x=-i

Find the zeros of x^4-1=0

The zeros of x^4-1=0 are x=1,x=-1,x=i,x=-i

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x^{4} - 1 = 0

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

Solution steps

x^{4} - 1 = 0

Move

1

to the right side

x^{4} = 1

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} = 1

Solve

u^{2} = 1 : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 1 : x = 1, x = - 1

Solve

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

The solutions are

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

\frac{49}{144}

7 x^{2} - 31 x + 12

\frac{2 x + 5}{3} = 11

- 15 x = 0

4 a^{2} - (5 b + 1)^{2}

What are the solutions to the equation x^4-1=0 ?
The solutions to the equation x^4-1=0 are x=1,x=-1,x=i,x=-i
Find the zeros of x^4-1=0
The zeros of x^4-1=0 are x=1,x=-1,x=i,x=-i