What are the solutions to the equation 4x(x-1)^2=1 ?

The solutions to the equation 4x(x-1)^2=1 are x\approx 1.41964…

Find the zeros of 4x(x-1)^2=1

The zeros of 4x(x-1)^2=1 are x\approx 1.41964…

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4 x (x - 1)^{2} = 1

x \approx 1.41964 \dots

Solution steps

4 x (x - 1)^{2} = 1

Expand

4 x (x - 1)^{2} : 4 x^{3} - 8 x^{2} + 4 x

4 x^{3} - 8 x^{2} + 4 x = 1

Move

1

to the left side

4 x^{3} - 8 x^{2} + 4 x - 1 = 0

Find one solution for

4 x^{3} - 8 x^{2} + 4 x - 1 = 0

using Newton-Raphson:

x \approx 1.41964 \dots

Apply long division:

\frac{4 x ^{3} - 8 x ^{2} + 4 x - 1}{x - 1.41964 \dots} = 4 x^{2} - 2.32142 \dots x + 0.70440 \dots

4 x^{2} - 2.32142 \dots x + 0.70440 \dots \approx 0

Find one solution for

4 x^{2} - 2.32142 \dots x + 0.70440 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.41964 \dots

(x + 1) (x + 2)^{2} (x^{2} - 6 x + 10) = 0

4 x^{3} - 3 x = 0

s^{3} = 1000

(2 A + 1) A^{66} = 0

(r - 1)^{2} (r + 1)^{3} = 0

What are the solutions to the equation 4x(x-1)^2=1 ?
The solutions to the equation 4x(x-1)^2=1 are x\approx 1.41964…
Find the zeros of 4x(x-1)^2=1
The zeros of 4x(x-1)^2=1 are x\approx 1.41964…