well, here's another tough one, please explain the steps ...
4(x – 1/x)² + 8(x + 1/x) – 29 = 0
[Ans: x=1/2, (- 9 ± √65)/ 4]
Its a nested quadratic :P
To see that more clearly First write $\displaystyle \left(x - \frac1{x}\right)^2 = \left(x + \frac1{x}\right)^2 - 4$
So
4(x – 1/x)² + 8(x + 1/x) – 29 = 4((x + 1/x)² - 4) + 8(x + 1/x) – 29 = 4(x + 1/x)² + 8(x + 1/x) – 45 = 0
Now the last equation is a quadratic in (x+1/x). So solve it. Once you get a couple of answers for that solve the equation "x+1/x = previous answer", which is another quadratic.