What are the solutions to the equation x^5+x=1 ?

The solutions to the equation x^5+x=1 are x\approx 0.75487…

Find the zeros of x^5+x=1

The zeros of x^5+x=1 are x\approx 0.75487…

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x^{5} + x = 1

x \approx 0.75487 \dots

Solution steps

x^{5} + x = 1

Move

1

to the left side

x^{5} + x - 1 = 0

Find one solution for

x^{5} + x - 1 = 0

using Newton-Raphson:

x \approx 0.75487 \dots

Apply long division:

\frac{x ^{5} + x - 1}{x - 0.75487 \dots} = x^{4} + 0.75487 \dots x^{3} + 0.56984 \dots x^{2} + 0.43015 \dots x + 1.32471 \dots

x^{4} + 0.75487 \dots x^{3} + 0.56984 \dots x^{2} + 0.43015 \dots x + 1.32471 \dots \approx 0

Find one solution for

x^{4} + 0.75487 \dots x^{3} + 0.56984 \dots x^{2} + 0.43015 \dots x + 1.32471 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.75487 \dots

- 35 x^{6} = (- 5 x^{2}) (B)

x^{3} - 7 x^{2} - 49 x + 343 = 0

3 x^{3} + 2 x^{2} + 27 x + 18 = 0

4 x^{3} - 12 x^{2} + 6 x = 0

(- 2 x^{2} - 5 x + 3) (3 a + x) = 0

What are the solutions to the equation x^5+x=1 ?
The solutions to the equation x^5+x=1 are x\approx 0.75487…
Find the zeros of x^5+x=1
The zeros of x^5+x=1 are x\approx 0.75487…