What is the answer to x^2+1/(x^2)+x+1/x =4 ?

The answer to x^2+1/(x^2)+x+1/x =4 is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2

Solve for x: x^2+1/(x^2)+x+1/x =4

The solution is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{2} + \frac{1}{x ^{2}} + x + \frac{1}{x} = 4

x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Decimal Notation

x = 1, x = - 0.38196 \dots, x = - 2.61803 \dots

Solution steps

x^{2} + \frac{1}{x ^{2}} + x + \frac{1}{x} = 4

Multiply by LCM

x^{4} + 1 + x^{3} + x = 4 x^{2}

Solve

x^{4} + 1 + x^{3} + x = 4 x^{2} : x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

\frac{5 x}{x - 5} - 1 = \frac{1}{x - 5}

\frac{5}{2 x + 1} = \frac{2}{x + 1}

x + \frac{7}{x} = - 8

\frac{1 - 2 y}{3 - y} + y = \frac{1}{y + 2}

\frac{m}{m + 9} = \frac{63}{22}

What is the answer to x^2+1/(x^2)+x+1/x =4 ?
The answer to x^2+1/(x^2)+x+1/x =4 is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2
Solve for x: x^2+1/(x^2)+x+1/x =4
The solution is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2