What are the solutions to the equation x(x+1)^2-1=0 ?

The solutions to the equation x(x+1)^2-1=0 are x\approx 0.46557…

Find the zeros of x(x+1)^2-1=0

The zeros of x(x+1)^2-1=0 are x\approx 0.46557…

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

x \approx 0.46557 \dots

Solution steps

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

Expand

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.46557 \dots

Apply long division:

\frac{x ^{3} + 2 x ^{2} + x - 1}{x - 0.46557 \dots} = x^{2} + 2.46557 \dots x + 2.14789 \dots

x^{2} + 2.46557 \dots x + 2.14789 \dots \approx 0

Find one solution for

x^{2} + 2.46557 \dots x + 2.14789 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.46557 \dots

x^{4} + 8 x^{2} + 15 = 0

4 y^{3} - 2 = y - 8 y^{2}

x^{3} - x - 3 = 0

- x + x^{3} = 0

z^{4} + 2 - 2 3 i = 0

What are the solutions to the equation x(x+1)^2-1=0 ?
The solutions to the equation x(x+1)^2-1=0 are x\approx 0.46557…
Find the zeros of x(x+1)^2-1=0
The zeros of x(x+1)^2-1=0 are x\approx 0.46557…