What are the solutions to the equation b^3-b=15 ?

The solutions to the equation b^3-b=15 are b\approx 2.60124…

Find the zeros of b^3-b=15

The zeros of b^3-b=15 are b\approx 2.60124…

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b^{3} - b = 15

b \approx 2.60124 \dots

Solution steps

b^{3} - b = 15

Move

15

to the left side

b^{3} - b - 15 = 0

Find one solution for

b^{3} - b - 15 = 0

using Newton-Raphson:

b \approx 2.60124 \dots

Apply long division:

\frac{b ^{3} - b - 15}{b - 2.60124 \dots} = b^{2} + 2.60124 \dots b + 5.76647 \dots

b^{2} + 2.60124 \dots b + 5.76647 \dots \approx 0

Find one solution for

b^{2} + 2.60124 \dots b + 5.76647 \dots = 0

using Newton-Raphson:

No Solution for

b \in R

The solution is

b \approx 2.60124 \dots

x^{3} - 23 x^{2} + 142 x - 12 = 0

(x) = (x^{2} + 7 x - 8)^{2}

- 3 (x - 1) + 8 (x^{3}) = 6 x + 7 - 5 x

0 = 4 x^{3} - 4 x^{2} - 4

- 4 x^{3} - 4 x = 0

What are the solutions to the equation b^3-b=15 ?
The solutions to the equation b^3-b=15 are b\approx 2.60124…
Find the zeros of b^3-b=15
The zeros of b^3-b=15 are b\approx 2.60124…