What are the solutions to the equation x^23x=x^2-2 ?

The solutions to the equation x^23x=x^2-2 are x\approx-0.77541…

Find the zeros of x^23x=x^2-2

The zeros of x^23x=x^2-2 are x\approx-0.77541…

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

x \approx - 0.77541 \dots

Solution steps

x^{2} \cdot 3 x = x^{2} - 2

Expand

x^{2} \cdot 3 x : 3 x^{3}

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

Move

2

to the left side

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

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.77541 \dots

Apply long division:

\frac{3 x ^{3} - x ^{2} + 2}{x + 0.77541 \dots} = 3 x^{2} - 3.32625 \dots x + 2.57924 \dots

3 x^{2} - 3.32625 \dots x + 2.57924 \dots \approx 0

Find one solution for

3 x^{2} - 3.32625 \dots x + 2.57924 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.77541 \dots

- x^{3} + 15 x^{2} + 91 x + 51 = 0

60 x^{4} - 120 x^{3} = 0

835 = 5 x^{3}

x^{4} + x^{3} - 3 x^{2} + 3 x - 1 = 0

w^{3} - 2 w^{2} + 2 - 2 = 0.2

What are the solutions to the equation x^23x=x^2-2 ?
The solutions to the equation x^23x=x^2-2 are x\approx-0.77541…
Find the zeros of x^23x=x^2-2
The zeros of x^23x=x^2-2 are x\approx-0.77541…