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

The solutions to the equation x^4+x=3 are x\approx 1.16403…,x\approx-1.45262…

Find the zeros of x^4+x=3

The zeros of x^4+x=3 are x\approx 1.16403…,x\approx-1.45262…

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x^{4} + x = 3

x \approx 1.16403 \dots, x \approx - 1.45262 \dots

Solution steps

x^{4} + x = 3

Move

3

to the left side

x^{4} + x - 3 = 0

Find one solution for

x^{4} + x - 3 = 0

using Newton-Raphson:

x \approx 1.16403 \dots

Apply long division:

\frac{x ^{4} + x - 3}{x - 1.16403 \dots} = x^{3} + 1.16403 \dots x^{2} + 1.35497 \dots x + 2.57724 \dots

x^{3} + 1.16403 \dots x^{2} + 1.35497 \dots x + 2.57724 \dots \approx 0

Find one solution for

x^{3} + 1.16403 \dots x^{2} + 1.35497 \dots x + 2.57724 \dots = 0

using Newton-Raphson:

x \approx - 1.45262 \dots

Apply long division:

\frac{x ^{3} + 1.16403 \dots x ^{2} + 1.35497 \dots x + 2.57724 \dots}{x + 1.45262 \dots} = x^{2} - 0.28859 \dots x + 1.77419 \dots

x^{2} - 0.28859 \dots x + 1.77419 \dots \approx 0

Find one solution for

x^{2} - 0.28859 \dots x + 1.77419 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.16403 \dots, x \approx - 1.45262 \dots

x^{3} = 13 x^{2} - 42 x

s^{3} + 3 s^{2} + 3 s - 7 = 0

4 x^{3} + 24 x + 36 = 0

x^{3} = 76

y^{6} - 3 y^{4} + 3 y^{2} - y = 0

What are the solutions to the equation x^4+x=3 ?
The solutions to the equation x^4+x=3 are x\approx 1.16403…,x\approx-1.45262…
Find the zeros of x^4+x=3
The zeros of x^4+x=3 are x\approx 1.16403…,x\approx-1.45262…