What are the solutions to the equation 9=x^3+x ?

The solutions to the equation 9=x^3+x are x\approx 1.92017…

Find the zeros of 9=x^3+x

The zeros of 9=x^3+x are x\approx 1.92017…

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9 = x^{3} + x

x \approx 1.92017 \dots

Solution steps

9 = x^{3} + x

Switch sides

x^{3} + x = 9

Move

9

to the left side

x^{3} + x - 9 = 0

Find one solution for

x^{3} + x - 9 = 0

using Newton-Raphson:

x \approx 1.92017 \dots

Apply long division:

\frac{x ^{3} + x - 9}{x - 1.92017 \dots} = x^{2} + 1.92017 \dots x + 4.68707 \dots

x^{2} + 1.92017 \dots x + 4.68707 \dots \approx 0

Find one solution for

x^{2} + 1.92017 \dots x + 4.68707 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.92017 \dots

63 x + 12 x^{2} - 3 x^{3} = 0

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

3 y^{4} - 5 y^{2} + 1 = 0

x^{4} - x^{2} + \frac{1}{8} = 0

x^{3} = 49 x

What are the solutions to the equation 9=x^3+x ?
The solutions to the equation 9=x^3+x are x\approx 1.92017…
Find the zeros of 9=x^3+x
The zeros of 9=x^3+x are x\approx 1.92017…