What are the solutions to the equation y^3-9y^2+27y=47 ?

The solutions to the equation y^3-9y^2+27y=47 are y\approx 5.71441…

Find the zeros of y^3-9y^2+27y=47

The zeros of y^3-9y^2+27y=47 are y\approx 5.71441…

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y^{3} - 9 y^{2} + 27 y = 47

y \approx 5.71441 \dots

Solution steps

y^{3} - 9 y^{2} + 27 y = 47

Move

47

to the left side

y^{3} - 9 y^{2} + 27 y - 47 = 0

Find one solution for

y^{3} - 9 y^{2} + 27 y - 47 = 0

using Newton-Raphson:

y \approx 5.71441 \dots

Apply long division:

\frac{y ^{3} - 9 y ^{2} + 27 y - 47}{y - 5.71441 \dots} = y^{2} - 3.28558 \dots y + 8.22481 \dots

y^{2} - 3.28558 \dots y + 8.22481 \dots \approx 0

Find one solution for

y^{2} - 3.28558 \dots y + 8.22481 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 5.71441 \dots

9 x^{8} - 9 = 0

x^{3} - x^{2} = 1

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

x^{3} + 3 x^{2} - 25 x + 21

x^{4} = 80

What are the solutions to the equation y^3-9y^2+27y=47 ?
The solutions to the equation y^3-9y^2+27y=47 are y\approx 5.71441…
Find the zeros of y^3-9y^2+27y=47
The zeros of y^3-9y^2+27y=47 are y\approx 5.71441…