What are the solutions to the equation x^5+x^3+x=2 ?

The solutions to the equation x^5+x^3+x=2 are x\approx 0.86558…

Find the zeros of x^5+x^3+x=2

The zeros of x^5+x^3+x=2 are x\approx 0.86558…

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

x \approx 0.86558 \dots

Solution steps

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

Move

2

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.86558 \dots

Apply long division:

\frac{x ^{5} + x ^{3} + x - 2}{x - 0.86558 \dots} = x^{4} + 0.86558 \dots x^{3} + 1.74923 \dots x^{2} + 1.51410 \dots x + 2.31058 \dots

x^{4} + 0.86558 \dots x^{3} + 1.74923 \dots x^{2} + 1.51410 \dots x + 2.31058 \dots \approx 0

Find one solution for

x^{4} + 0.86558 \dots x^{3} + 1.74923 \dots x^{2} + 1.51410 \dots x + 2.31058 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.86558 \dots

x^{12} = 2

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

z^{4} = - 8 - 83 i

5 = x^{3}

y^{4} + 3 y^{3} - 2 y^{2} - y + 1 = 0

What are the solutions to the equation x^5+x^3+x=2 ?
The solutions to the equation x^5+x^3+x=2 are x\approx 0.86558…
Find the zeros of x^5+x^3+x=2
The zeros of x^5+x^3+x=2 are x\approx 0.86558…