What are the solutions to the equation (x+1)(x^2-2)=(x+3)3 ?

The solutions to the equation (x+1)(x^2-2)=(x+3)3 are x\approx 2.58347…

Find the zeros of (x+1)(x^2-2)=(x+3)3

The zeros of (x+1)(x^2-2)=(x+3)3 are x\approx 2.58347…

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(x + 1) (x^{2} - 2) = (x + 3) 3

x \approx 2.58347 \dots

Solution steps

(x + 1) (x^{2} - 2) = (x + 3) \cdot 3

Expand

(x + 1) (x^{2} - 2) : x^{3} - 2 x + x^{2} - 2

Expand

(x + 3) \cdot 3 : 3 x + 9

x^{3} - 2 x + x^{2} - 2 = 3 x + 9

Move

9

to the left side

x^{3} + x^{2} - 2 x - 11 = 3 x

Move

3 x

to the left side

x^{3} + x^{2} - 5 x - 11 = 0

Find one solution for

x^{3} + x^{2} - 5 x - 11 = 0

using Newton-Raphson:

x \approx 2.58347 \dots

Apply long division:

\frac{x ^{3} + x ^{2} - 5 x - 11}{x - 2.58347 \dots} = x^{2} + 3.58347 \dots x + 4.25782 \dots

x^{2} + 3.58347 \dots x + 4.25782 \dots \approx 0

Find one solution for

x^{2} + 3.58347 \dots x + 4.25782 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.58347 \dots

5 x^{4} - 20 x^{2} - 1 = 0

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

x^{4} = - 16

(- 1) (6 x^{3} + x^{2} + x - 1) = 0

y, 27 x^{3} + y^{3} + z^{3} = 9 x \cdot z

What are the solutions to the equation (x+1)(x^2-2)=(x+3)3 ?
The solutions to the equation (x+1)(x^2-2)=(x+3)3 are x\approx 2.58347…
Find the zeros of (x+1)(x^2-2)=(x+3)3
The zeros of (x+1)(x^2-2)=(x+3)3 are x\approx 2.58347…