What are the solutions to the equation x^3-[x]=3 ?

The solutions to the equation x^3-[x]=3 are x\approx 1.67169…

Find the zeros of x^3-[x]=3

The zeros of x^3-[x]=3 are x\approx 1.67169…

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Popular >

x^{3} - [x] = 3

x \approx 1.67169 \dots

Solution steps

x^{3} - [x] = 3

Expand

x^{3} - (x) : x^{3} - x

x^{3} - x = 3

Move

3

to the left side

x^{3} - x - 3 = 0

Find one solution for

x^{3} - x - 3 = 0

using Newton-Raphson:

x \approx 1.67169 \dots

Apply long division:

\frac{x ^{3} - x - 3}{x - 1.67169 \dots} = x^{2} + 1.67169 \dots x + 1.79458 \dots

x^{2} + 1.67169 \dots x + 1.79458 \dots \approx 0

Find one solution for

x^{2} + 1.67169 \dots x + 1.79458 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.67169 \dots

x^{4} - 13 x + 36 = 0

x^{4} + 17 x^{2} + 16 = 0

x^{6} + 64 = 0

x^{3} + 3 x^{2} = 16 x + 48

x^{252} = 0.7

What are the solutions to the equation x^3-[x]=3 ?
The solutions to the equation x^3-[x]=3 are x\approx 1.67169…
Find the zeros of x^3-[x]=3
The zeros of x^3-[x]=3 are x\approx 1.67169…