What is the answer to 0=6x^2-2/(x^2)+13/2 ?

The answer to 0=6x^2-2/(x^2)+13/2 is x= 1/2 ,x=-1/2 ,x= 2/(sqrt(3))i,x=-2/(sqrt(3))i

Solve for x: 0=6x^2-2/(x^2)+13/2

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

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0 = 6 x^{2} - \frac{2}{x ^{2}} + \frac{13}{2}

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

Solution steps

0 = 6 x^{2} - \frac{2}{x ^{2}} + \frac{13}{2}

Multiply by LCM

0 = 12 x^{4} - 4 + 13 x^{2}

Solve

0 = 12 x^{4} - 4 + 13 x^{2} : x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{2}{3} i, x = - \frac{2}{3} i

\frac{4 x ^{2} - 3 x + 5}{x ^{2} - 2 x + 13} = 2

x + \frac{1}{x} = \frac{6 5}{5}

5 x - \frac{1}{x} = 4

4 x - \frac{36}{x} = 0

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

What is the answer to 0=6x^2-2/(x^2)+13/2 ?
The answer to 0=6x^2-2/(x^2)+13/2 is x= 1/2 ,x=-1/2 ,x= 2/(sqrt(3))i,x=-2/(sqrt(3))i
Solve for x: 0=6x^2-2/(x^2)+13/2
The solution is x= 1/2 ,x=-1/2 ,x= 2/(sqrt(3))i,x=-2/(sqrt(3))i