What are the solutions to the equation x^4=2-x ?

The solutions to the equation x^4=2-x are x=1,x\approx-1.35320…

Find the zeros of x^4=2-x

The zeros of x^4=2-x are x=1,x\approx-1.35320…

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x^{4} = 2 - x

x = 1, x \approx - 1.35320 \dots

Solution steps

x^{4} = 2 - x

Move

x

to the left side

x^{4} + x = 2

Move

2

to the left side

x^{4} + x - 2 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + x^{2} + x + 2 = 0 : x \approx - 1.35320 \dots

The solutions are

x = 1, x \approx - 1.35320 \dots

y^{3} + 3 y^{2} = 36 y + 108

v = \frac{4}{3} π r^{3}, r

x^{3} - 7 x^{2} + 7 x + 15 = 0

x^{3} + 6 x + 4 = 0

(x - 2)^{3} + 18 = 530

What are the solutions to the equation x^4=2-x ?
The solutions to the equation x^4=2-x are x=1,x\approx-1.35320…
Find the zeros of x^4=2-x
The zeros of x^4=2-x are x=1,x\approx-1.35320…