What are the solutions to the equation d^4-81=0 ?

The solutions to the equation d^4-81=0 are d=3,d=-3,d=3i,d=-3i

Find the zeros of d^4-81=0

The zeros of d^4-81=0 are d=3,d=-3,d=3i,d=-3i

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d^{4} - 81 = 0

d = 3, d = - 3, d = 3 i, d = - 3 i

Solution steps

d^{4} - 81 = 0

Move

81

to the right side

d^{4} = 81

Rewrite the equation with

u = d^{2}

and

u^{2} = d^{4}

u^{2} = 81

Solve

u^{2} = 81 : u = 81, u = - 81

u = 81, u = - 81

Substitute back

u = d^{2},

solve for

d

Solve

d^{2} = 81 : d = 3, d = - 3

Solve

d^{2} = - 81 : d = 3 i, d = - 3 i

The solutions are

d = 3, d = - 3, d = 3 i, d = - 3 i

x^{6} + 3 x^{3} - 4 = 0

2 x^{4} + 3 x^{2} - 20 = 0

x^{4} - 2 x^{2} - 15 = 0

λ^{3} + 2 λ^{2} - λ - 2 = 0

x^{5} + x^{3} + 1 = 0

What are the solutions to the equation d^4-81=0 ?
The solutions to the equation d^4-81=0 are d=3,d=-3,d=3i,d=-3i
Find the zeros of d^4-81=0
The zeros of d^4-81=0 are d=3,d=-3,d=3i,d=-3i