If $$x^4 - 6x^2 - 1 = 0$$, then the value of $$x^6 - 5x^2 + \frac{5}{x^2} - \frac{1}{x^6} + 5$$ is:
Dividing by x^2
we get :$$x^2-\frac{1}{x^2}\ =6$$
Now taking cube
we get $$x^6-\frac{1}{x^6}-18\ =216$$
so $$x^6-\frac{1}{x^6}=234$$
Now the given expression will be $$x^6-\frac{1}{x^6}-5\left(x^2-\frac{1}{x^2}\right)+5$$
we get 234-30+5 =209
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