What are the solutions to the equation (y(y-1)^2)/(1.5)=1 ?

The solutions to the equation (y(y-1)^2)/(1.5)=1 are y\approx 1.89070…

Find the zeros of (y(y-1)^2)/(1.5)=1

The zeros of (y(y-1)^2)/(1.5)=1 are y\approx 1.89070…

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\frac{y ( y - 1 ) ^{2}}{1.5} = 1

y \approx 1.89070 \dots

Solution steps

\frac{y ( y - 1 ) ^{2}}{1.5} = 1

Multiply both sides by

1.5

y (y - 1)^{2} = 1.5

Expand

y (y - 1)^{2} : y^{3} - 2 y^{2} + y

y^{3} - 2 y^{2} + y = 1.5

Move

1.5

to the left side

y^{3} - 2 y^{2} + y - 1.5 = 0

Find one solution for

y^{3} - 2 y^{2} + y - 1.5 = 0

using Newton-Raphson:

y \approx 1.89070 \dots

Apply long division:

\frac{y ^{3} - 2 y ^{2} + y - 1.5}{y - 1.89070 \dots} = y^{2} - 0.10929 \dots y + 0.79335 \dots

y^{2} - 0.10929 \dots y + 0.79335 \dots \approx 0

Find one solution for

y^{2} - 0.10929 \dots y + 0.79335 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 1.89070 \dots

x^{3} - 13 x^{2} - 115 x + 138 = 0

z^{4} + 2 - 23 i = 0

0 = t^{3} - 6 t^{2} + 9 t + 5

x^{3} - x^{2} + 1 = - 6

2 x^{4} - 16 x = 0

What are the solutions to the equation (y(y-1)^2)/(1.5)=1 ?
The solutions to the equation (y(y-1)^2)/(1.5)=1 are y\approx 1.89070…
Find the zeros of (y(y-1)^2)/(1.5)=1
The zeros of (y(y-1)^2)/(1.5)=1 are y\approx 1.89070…