What are the solutions to the equation x^4+2x+1=3 ?

The solutions to the equation x^4+2x+1=3 are x\approx 0.79762…,x\approx-1.49453…

Find the zeros of x^4+2x+1=3

The zeros of x^4+2x+1=3 are x\approx 0.79762…,x\approx-1.49453…

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x^{4} + 2 x + 1 = 3

x \approx 0.79762 \dots, x \approx - 1.49453 \dots

Solution steps

x^{4} + 2 x + 1 = 3

Move

3

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.79762 \dots

Apply long division:

\frac{x ^{4} + 2 x - 2}{x - 0.79762 \dots} = x^{3} + 0.79762 \dots x^{2} + 0.63620 \dots x + 2.50744 \dots

x^{3} + 0.79762 \dots x^{2} + 0.63620 \dots x + 2.50744 \dots \approx 0

Find one solution for

x^{3} + 0.79762 \dots x^{2} + 0.63620 \dots x + 2.50744 \dots = 0

using Newton-Raphson:

x \approx - 1.49453 \dots

Apply long division:

\frac{x ^{3} + 0.79762 \dots x ^{2} + 0.63620 \dots x + 2.50744 \dots}{x + 1.49453 \dots} = x^{2} - 0.69690 \dots x + 1.67775 \dots

x^{2} - 0.69690 \dots x + 1.67775 \dots \approx 0

Find one solution for

x^{2} - 0.69690 \dots x + 1.67775 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.79762 \dots, x \approx - 1.49453 \dots

(x - 3) (x^{2} + 1) = 0

c^{3} + 2 c = 2 c^{5}

n x^{3} + 8 = 11

0 = \frac{1}{6} x^{3} - x

x^{4} + 2 x^{3} - 3 x^{2} + 10 x + 25 = 0

What are the solutions to the equation x^4+2x+1=3 ?
The solutions to the equation x^4+2x+1=3 are x\approx 0.79762…,x\approx-1.49453…
Find the zeros of x^4+2x+1=3
The zeros of x^4+2x+1=3 are x\approx 0.79762…,x\approx-1.49453…