What are the solutions to the equation 9=x^5+x^3+x ?

The solutions to the equation 9=x^5+x^3+x are x\approx 1.37947…

Find the zeros of 9=x^5+x^3+x

The zeros of 9=x^5+x^3+x are x\approx 1.37947…

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

x \approx 1.37947 \dots

Solution steps

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

Switch sides

x^{5} + x^{3} + x = 9

Move

9

to the left side

x^{5} + x^{3} + x - 9 = 0

Find one solution for

x^{5} + x^{3} + x - 9 = 0

using Newton-Raphson:

x \approx 1.37947 \dots

Apply long division:

\frac{x ^{5} + x ^{3} + x - 9}{x - 1.37947 \dots} = x^{4} + 1.37947 \dots x^{3} + 2.90295 \dots x^{2} + 4.00456 \dots x + 6.52420 \dots

x^{4} + 1.37947 \dots x^{3} + 2.90295 \dots x^{2} + 4.00456 \dots x + 6.52420 \dots \approx 0

Find one solution for

x^{4} + 1.37947 \dots x^{3} + 2.90295 \dots x^{2} + 4.00456 \dots x + 6.52420 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.37947 \dots

3 x^{3} - 4 x^{2} - 48 x + 64 = 0

10000 = 1 x^{10}

5 x^{4} - 40 x = 0

555 = 5 x^{3}

(2 x + 1)^{4} + 4 (2 x + 1)^{2} = 12

What are the solutions to the equation 9=x^5+x^3+x ?
The solutions to the equation 9=x^5+x^3+x are x\approx 1.37947…
Find the zeros of 9=x^5+x^3+x
The zeros of 9=x^5+x^3+x are x\approx 1.37947…