What are the solutions to the equation (x+1)^4+(x+1)^2-6=0 ?

The solutions to the equation (x+1)^4+(x+1)^2-6=0 are x\approx 0.41421…,x\approx-2.41421…

Find the zeros of (x+1)^4+(x+1)^2-6=0

The zeros of (x+1)^4+(x+1)^2-6=0 are x\approx 0.41421…,x\approx-2.41421…

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(x + 1)^{4} + (x + 1)^{2} - 6 = 0

x \approx 0.41421 \dots, x \approx - 2.41421 \dots

Solution steps

(x + 1)^{4} + (x + 1)^{2} - 6 = 0

Expand

(x + 1)^{4} + (x + 1)^{2} - 6 : x^{4} + 4 x^{3} + 7 x^{2} + 6 x - 4

x^{4} + 4 x^{3} + 7 x^{2} + 6 x - 4 = 0

Find one solution for

x^{4} + 4 x^{3} + 7 x^{2} + 6 x - 4 = 0

using Newton-Raphson:

x \approx 0.41421 \dots

Apply long division:

\frac{x ^{4} + 4 x ^{3} + 7 x ^{2} + 6 x - 4}{x - 0.41421 \dots} = x^{3} + 4.41421 \dots x^{2} + 8.82842 \dots x + 9.65685 \dots

x^{3} + 4.41421 \dots x^{2} + 8.82842 \dots x + 9.65685 \dots \approx 0

Find one solution for

x^{3} + 4.41421 \dots x^{2} + 8.82842 \dots x + 9.65685 \dots = 0

using Newton-Raphson:

x \approx - 2.41421 \dots

Apply long division:

\frac{x ^{3} + 4.41421 \dots x ^{2} + 8.82842 \dots x + 9.65685 \dots}{x + 2.41421 \dots} = x^{2} + 2 x + 4.00000 \dots

x^{2} + 2 x + 4.00000 \dots \approx 0

Find one solution for

x^{2} + 2 x + 4.00000 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.41421 \dots, x \approx - 2.41421 \dots

5 y^{4} - 15 y^{2} + 4 = 0

16 x^{3} - 48 x^{2} - 200 = 0

i z^{3} + 8 = 0

- 2 x^{4} + 13 x^{3} - 21 x^{2} + 2 x + 8 = 0

25 x^{3} - 100 x^{2} - 16 x + 64 = 0

What are the solutions to the equation (x+1)^4+(x+1)^2-6=0 ?
The solutions to the equation (x+1)^4+(x+1)^2-6=0 are x\approx 0.41421…,x\approx-2.41421…
Find the zeros of (x+1)^4+(x+1)^2-6=0
The zeros of (x+1)^4+(x+1)^2-6=0 are x\approx 0.41421…,x\approx-2.41421…