What are the solutions to the equation sqrt(3)b=9(b^3+3) ?

The solutions to the equation sqrt(3)b=9(b^3+3) are b\approx-1.48671…

Find the zeros of sqrt(3)b=9(b^3+3)

The zeros of sqrt(3)b=9(b^3+3) are b\approx-1.48671…

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3 b = 9 (b^{3} + 3)

b \approx - 1.48671 \dots

Solution steps

3 b = 9 (b^{3} + 3)

Expand

9 (b^{3} + 3) : 9 b^{3} + 27

3 b = 9 b^{3} + 27

Switch sides

9 b^{3} + 27 = 3 b

Move

3 b

to the left side

9 b^{3} + 27 - 3 b = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

9 b^{3} - 3 b + 27 = 0

Find one solution for

9 b^{3} - 1.73205 \dots b + 27 = 0

using Newton-Raphson:

b \approx - 1.48671 \dots

Apply long division:

\frac{9 b ^{3} - 3 b + 27}{b + 1.48671 \dots} = 9 b^{2} - 13.38043 \dots b + 18.16084 \dots

9 b^{2} - 13.38043 \dots b + 18.16084 \dots \approx 0

Find one solution for

9 b^{2} - 13.38043 \dots b + 18.16084 \dots = 0

using Newton-Raphson:

No Solution for

b \in R

The solution is

b \approx - 1.48671 \dots

x, x^{4} + 4 y^{2} = z^{2}

y^{(10)} = 0

27 x^{3} + 27 x^{2} + 9 x = - 1

6 x^{3} + 43 x^{2} + 43 x + 6 = 0

(x^{2} + 8)^{2} - (x^{2} + 8) - 72 = 0

What are the solutions to the equation sqrt(3)b=9(b^3+3) ?
The solutions to the equation sqrt(3)b=9(b^3+3) are b\approx-1.48671…
Find the zeros of sqrt(3)b=9(b^3+3)
The zeros of sqrt(3)b=9(b^3+3) are b\approx-1.48671…