What are the solutions to the equation 5y-62=y-2-y^3 ?

The solutions to the equation 5y-62=y-2-y^3 are y\approx 3.57521…

Find the zeros of 5y-62=y-2-y^3

The zeros of 5y-62=y-2-y^3 are y\approx 3.57521…

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5 y - 62 = y - 2 - y^{3}

y \approx 3.57521 \dots

Solution steps

5 y - 62 = y - 2 - y^{3}

Switch sides

y - 2 - y^{3} = 5 y - 62

Move

62

to the left side

- y^{3} + y + 60 = 5 y

Move

5 y

to the left side

- y^{3} - 4 y + 60 = 0

Find one solution for

- y^{3} - 4 y + 60 = 0

using Newton-Raphson:

y \approx 3.57521 \dots

Apply long division:

\frac{- y ^{3} - 4 y + 60}{y - 3.57521 \dots} = - y^{2} - 3.57521 \dots y - 16.78218 \dots

- y^{2} - 3.57521 \dots y - 16.78218 \dots \approx 0

Find one solution for

- y^{2} - 3.57521 \dots y - 16.78218 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 3.57521 \dots

12 x^{3} + 18 x^{2} - 18 x - 12 = 0

(5 y^{4})^{3} = 125 y^{24}

z^{8} + 1 = 3 i

2 x^{3} - 6 x^{2} + 2 x + 8 = 0

5 x^{3} + 2 x^{3} + 3 x^{6} = 39

What are the solutions to the equation 5y-62=y-2-y^3 ?
The solutions to the equation 5y-62=y-2-y^3 are y\approx 3.57521…
Find the zeros of 5y-62=y-2-y^3
The zeros of 5y-62=y-2-y^3 are y\approx 3.57521…