What are the solutions to the equation x^6+2x^2+1=0 ?

The solutions to the equation x^6+2x^2+1=0 are No Solution for x\in\mathbb{R}

Find the zeros of x^6+2x^2+1=0

The zeros of x^6+2x^2+1=0 are No Solution for x\in\mathbb{R}

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x^{6} + 2 x^{2} + 1 = 0

No Solution for x \in R

Solution steps

x^{6} + 2 x^{2} + 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{3} = x^{6}

u^{3} + 2 u + 1 = 0

Solve

u^{3} + 2 u + 1 = 0 : u \approx - 0.45339 \dots

u \approx - 0.45339 \dots

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = - 0.45339 \dots :

No Solution for

x \in R

The solution is

No Solution for x \in R

2 x^{3} - 28 x^{2} + 80 x = 0

s^{4} + 9 s^{3} + 32 s^{2} + 60 s = 0

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

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

9 x^{4} - 730 x^{2} + 81 = 0

What are the solutions to the equation x^6+2x^2+1=0 ?
The solutions to the equation x^6+2x^2+1=0 are No Solution for x\in\mathbb{R}
Find the zeros of x^6+2x^2+1=0
The zeros of x^6+2x^2+1=0 are No Solution for x\in\mathbb{R}