What are the solutions to the equation x^{10}=-x,x ?

The solutions to the equation x^{10}=-x,x are

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{10}=-x,x

x^{10} = - x, x

x = 0, x = - 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}, x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9}), x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

Solution steps

x^{10} = - x, x

Move

x

to the left side

x^{10} + x = 0

Factor

x^{10} + x : x (x + 1) (x^{2} - x + 1) (x^{6} - x^{3} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - x + 1 = 0 : x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Solve

x^{6} - x^{3} + 1 = 0 : x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9}), x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

The solutions are

x = 0, x = - 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}, x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9}), x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

x^{4} - 15 x^{2} + 50 = 0

x^{3} + 7 x^{2} + 9 x - 17 = 0

x, 8 x^{3} - 27 y^{2} = 0

4 x (7 + 3) = (4 x^{7}) + (4 x^{3})

\frac{16 ( 16 + 1 )}{2} = a^{3}

What are the solutions to the equation x^{10}=-x,x ?
The solutions to the equation x^{10}=-x,x are
Find the zeros of x^{10}=-x,x
The zeros of x^{10}=-x,x are