What are the solutions to the equation r^8+8r^4+16=0 ?

The solutions to the equation r^8+8r^4+16=0 are r=1+i,r=-1-i,r=1-i,r=-1+i

Find the zeros of r^8+8r^4+16=0

The zeros of r^8+8r^4+16=0 are r=1+i,r=-1-i,r=1-i,r=-1+i

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r^{8} + 8 r^{4} + 16 = 0

r = 1 + i, r = - 1 - i, r = 1 - i, r = - 1 + i

Solution steps

r^{8} + 8 r^{4} + 16 = 0

Rewrite the equation with

u = r^{2}, u^{2} = r^{4}

and

u^{4} = r^{8}

u^{4} + 8 u^{2} + 16 = 0

Solve

u^{4} + 8 u^{2} + 16 = 0 : u = 2 i, u = - 2 i

u = 2 i, u = - 2 i

Substitute back

u = r^{2},

solve for

r

Solve

r^{2} = 2 i : r = 1 + i, r = - 1 - i

Solve

r^{2} = - 2 i : r = 1 - i, r = - 1 + i

The solutions are

r = 1 + i, r = - 1 - i, r = 1 - i, r = - 1 + i

x^{4} + 2 x^{3} - 9 x^{2} - 2 x + 8 = 0

- x^{3} - 6 x^{2} + 48 x + 278

2 x^{3} - 11 x^{2} + 12 x + 9

2 x^{4} - x^{3} - 7 x^{2} + x + 2 = 0

x^{4} - 5 x^{2} - 36 = 0

What are the solutions to the equation r^8+8r^4+16=0 ?
The solutions to the equation r^8+8r^4+16=0 are r=1+i,r=-1-i,r=1-i,r=-1+i
Find the zeros of r^8+8r^4+16=0
The zeros of r^8+8r^4+16=0 are r=1+i,r=-1-i,r=1-i,r=-1+i