What are the solutions to the equation x(x^2-3)^3-2=1785 ?

The solutions to the equation x(x^2-3)^3-2=1785 are x\approx 3.33500…

Find the zeros of x(x^2-3)^3-2=1785

The zeros of x(x^2-3)^3-2=1785 are x\approx 3.33500…

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x (x^{2} - 3)^{3} - 2 = 1785

x \approx 3.33500 \dots

Solution steps

x (x^{2} - 3)^{3} - 2 = 1785

Expand

x (x^{2} - 3)^{3} - 2 : x^{7} - 9 x^{5} + 27 x^{3} - 27 x - 2

x^{7} - 9 x^{5} + 27 x^{3} - 27 x - 2 = 1785

Move

1785

to the left side

x^{7} - 9 x^{5} + 27 x^{3} - 27 x - 1787 = 0

Find one solution for

x^{7} - 9 x^{5} + 27 x^{3} - 27 x - 1787 = 0

using Newton-Raphson:

x \approx 3.33500 \dots

Apply long division:

\frac{x ^{7} - 9 x ^{5} + 27 x ^{3} - 27 x - 1787}{x - 3.33500 \dots} = x^{6} + 3.33500 \dots x^{5} + 2.12224 \dots x^{4} + 7.07769 \dots x^{3} + 50.60413 \dots x^{2} + 168.76494 \dots x + 535.83159 \dots

x^{6} + 3.33500 \dots x^{5} + 2.12224 \dots x^{4} + 7.07769 \dots x^{3} + 50.60413 \dots x^{2} + 168.76494 \dots x + 535.83159 \dots \approx 0

Find one solution for

x^{6} + 3.33500 \dots x^{5} + 2.12224 \dots x^{4} + 7.07769 \dots x^{3} + 50.60413 \dots x^{2} + 168.76494 \dots x + 535.83159 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 3.33500 \dots

\frac{3}{16} = 3 r^{4}

x^{4} - 7 x^{2} - 5 = 0

2 x^{3} + 5 x + 7 = 0

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

x^{3} + 12 x^{2} + 29 \cdot + 18 = 0

What are the solutions to the equation x(x^2-3)^3-2=1785 ?
The solutions to the equation x(x^2-3)^3-2=1785 are x\approx 3.33500…
Find the zeros of x(x^2-3)^3-2=1785
The zeros of x(x^2-3)^3-2=1785 are x\approx 3.33500…