What are the solutions to the equation x^3+x^2=1 ?

The solutions to the equation x^3+x^2=1 are x\approx 0.75487…

Find the zeros of x^3+x^2=1

The zeros of x^3+x^2=1 are x\approx 0.75487…

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

x \approx 0.75487 \dots

Solution steps

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

Move

1

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.75487 \dots

Apply long division:

\frac{x ^{3} + x ^{2} - 1}{x - 0.75487 \dots} = x^{2} + 1.75487 \dots x + 1.32471 \dots

x^{2} + 1.75487 \dots x + 1.32471 \dots \approx 0

Find one solution for

x^{2} + 1.75487 \dots x + 1.32471 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.75487 \dots

(m + 1)^{3} = 0

2 x^{3} - 250 = 0

x^{4} - 8 x^{2} + 16 = 0

5 x^{5} - 44 x^{3} - 9 x = 0

1 x^{4} - 7^{2} x - 4 = 0

What are the solutions to the equation x^3+x^2=1 ?
The solutions to the equation x^3+x^2=1 are x\approx 0.75487…
Find the zeros of x^3+x^2=1
The zeros of x^3+x^2=1 are x\approx 0.75487…