What are the solutions to the equation 81x^4=3x ?

The solutions to the equation 81x^4=3x are x=0,x= 1/3 ,x=-1/6+i(sqrt(3))/6 ,x=-1/6-i(sqrt(3))/6

Find the zeros of 81x^4=3x

The zeros of 81x^4=3x are x=0,x= 1/3 ,x=-1/6+i(sqrt(3))/6 ,x=-1/6-i(sqrt(3))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

81 x^{4} = 3 x

x = 0, x = \frac{1}{3}, x = - \frac{1}{6} + i \frac{3}{6}, x = - \frac{1}{6} - i \frac{3}{6}

Solution steps

81 x^{4} = 3 x

Move

3 x

to the left side

81 x^{4} - 3 x = 0

Factor

81 x^{4} - 3 x : 3 x (3 x - 1) (9 x^{2} + 3 x + 1)

3 x (3 x - 1) (9 x^{2} + 3 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x - 1 = 0 or 9 x^{2} + 3 x + 1 = 0

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

9 x^{2} + 3 x + 1 = 0 : x = - \frac{1}{6} + i \frac{3}{6}, x = - \frac{1}{6} - i \frac{3}{6}

The solutions are

x = 0, x = \frac{1}{3}, x = - \frac{1}{6} + i \frac{3}{6}, x = - \frac{1}{6} - i \frac{3}{6}

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

x^{3} + x = 130

x^{4} - 5 x^{2} + 1

z^{4} + z = 0

(1 + x)^{12} = 2.12

What are the solutions to the equation 81x^4=3x ?
The solutions to the equation 81x^4=3x are x=0,x= 1/3 ,x=-1/6+i(sqrt(3))/6 ,x=-1/6-i(sqrt(3))/6
Find the zeros of 81x^4=3x
The zeros of 81x^4=3x are x=0,x= 1/3 ,x=-1/6+i(sqrt(3))/6 ,x=-1/6-i(sqrt(3))/6