What are the solutions to the equation 2y^3+6y=1 ?

The solutions to the equation 2y^3+6y=1 are y\approx 0.16516…

Find the zeros of 2y^3+6y=1

The zeros of 2y^3+6y=1 are y\approx 0.16516…

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2 y^{3} + 6 y = 1

y \approx 0.16516 \dots

Solution steps

2 y^{3} + 6 y = 1

Move

1

to the left side

2 y^{3} + 6 y - 1 = 0

Find one solution for

2 y^{3} + 6 y - 1 = 0

using Newton-Raphson:

y \approx 0.16516 \dots

Apply long division:

\frac{2 y ^{3} + 6 y - 1}{y - 0.16516 \dots} = 2 y^{2} + 0.33032 \dots y + 6.05455 \dots

2 y^{2} + 0.33032 \dots y + 6.05455 \dots \approx 0

Find one solution for

2 y^{2} + 0.33032 \dots y + 6.05455 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 0.16516 \dots

5 x - 17 = - x^{7}

x^{3} - 2 x^{2} - 25 x + 50

4 x^{3} + 2 x - 10 = 0

120 x^{2} - 15 x^{4} = 0

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

What are the solutions to the equation 2y^3+6y=1 ?
The solutions to the equation 2y^3+6y=1 are y\approx 0.16516…
Find the zeros of 2y^3+6y=1
The zeros of 2y^3+6y=1 are y\approx 0.16516…