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## Homework Statement

Solve this equation, and find x.

[tex]6x^5-5x^4-29x^2-5x+6=0[/tex]

## Homework Equations

if [tex]x= \alpha[/tex] is root of the symmetric equation, then [tex]x= \frac{1}{\alpha}[/tex], is also root of the symmetric equation

## The Attempt at a Solution

I tried first to write like this

[tex]6x^5-5x^4-30x^2+x^2-5x+6=0[/tex]

and then multiplying by five

[tex]30x^5-25x^4-150x^2+5x^2-25x+30=0[/tex]

then trying to divide with [tex]x^3[/tex]

[tex]30x^2-25x-150 \frac{1}{x} +5 \frac{1}{x} -25 \frac{1}{x^2}+30 \frac{1}{x^3}=0[/tex]

then adding [tex]-30x^3+30x^3[/tex]

[tex]-30x^3+30x^3 + 30x^2-25x-150 \frac{1}{x} +5 \frac{1}{x} -25 \frac{1}{x^2}+30 \frac{1}{x^3}=0[/tex]

And I am stuck in here. Please help me. Thank you.