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

The solutions to the equation (sqrt(2))^2=(x)(x+1)^2 are x\approx 0.69562…

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

The zeros of (sqrt(2))^2=(x)(x+1)^2 are x\approx 0.69562…

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

x \approx 0.69562 \dots

Solution steps

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

Expand

(2)^{2} : 2

Expand

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

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

Switch sides

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

Move

2

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.69562 \dots

Apply long division:

\frac{x ^{3} + 2 x ^{2} + x - 2}{x - 0.69562 \dots} = x^{2} + 2.69562 \dots x + 2.87512 \dots

x^{2} + 2.69562 \dots x + 2.87512 \dots \approx 0

Find one solution for

x^{2} + 2.69562 \dots x + 2.87512 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.69562 \dots

5 k^{3} = - 10 k^{2} + 5 k + 10

x^{4} + x^{2} = 20

s^{4} + 9 s^{2} + 14 = 0

0 = x^{2} - 2 x^{3} - 10 x + 11

3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

What are the solutions to the equation (sqrt(2))^2=(x)(x+1)^2 ?
The solutions to the equation (sqrt(2))^2=(x)(x+1)^2 are x\approx 0.69562…
Find the zeros of (sqrt(2))^2=(x)(x+1)^2
The zeros of (sqrt(2))^2=(x)(x+1)^2 are x\approx 0.69562…