What are the solutions to the equation x^1+x^2+x^3=4 ?

The solutions to the equation x^1+x^2+x^3=4 are x\approx 1.15091…

Find the zeros of x^1+x^2+x^3=4

The zeros of x^1+x^2+x^3=4 are x\approx 1.15091…

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

x \approx 1.15091 \dots

Solution steps

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

Refine

x + x^{2} + x^{3} = 4

Move

4

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.15091 \dots

Apply long division:

\frac{x ^{3} + x ^{2} + x - 4}{x - 1.15091 \dots} = x^{2} + 2.15091 \dots x + 3.47550 \dots

x^{2} + 2.15091 \dots x + 3.47550 \dots \approx 0

Find one solution for

x^{2} + 2.15091 \dots x + 3.47550 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.15091 \dots

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

(x + 1)^{3} = 0

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

x^{4} = 5 x^{2} - 6

b^{3} + b^{2} = 108

What are the solutions to the equation x^1+x^2+x^3=4 ?
The solutions to the equation x^1+x^2+x^3=4 are x\approx 1.15091…
Find the zeros of x^1+x^2+x^3=4
The zeros of x^1+x^2+x^3=4 are x\approx 1.15091…