What are the solutions to the equation 81=r^4 ?

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

Find the zeros of 81=r^4

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

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81 = r^{4}

r = 3, r = - 3, r = 3 i, r = - 3 i

Solution steps

81 = r^{4}

Switch sides

r^{4} = 81

Rewrite the equation with

u = r^{2}

and

u^{2} = r^{4}

u^{2} = 81

Solve

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

u = 81, u = - 81

Substitute back

u = r^{2},

solve for

r

Solve

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

Solve

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

The solutions are

r = 3, r = - 3, r = 3 i, r = - 3 i

x, 3 x^{3} + y^{4} = cy

X^{3} + 3 X^{2} - 4 X - 12 = 0

x^{5} - x^{3} - 3 x - 2 = 0

x^{3} - 15 = - 7

0 = x^{3} - x^{2} - 7 x + 7

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