To solve the equation `x^2+1/x^2-3(x-1/x)-2=0` we can use a very interesting trick that comes up occasionally. Notice that the first two terms can be combined with the last term to get
`x^2-2+1/x^2-3(x-1/x)=0` now let `u=x-1/x`
but this means that `u^2=x^2-2+1/x^2` since the x's cancel out in the middle term.
The equation now becomes
which has two solutions u=0 and u=3.
Look at the first:
`x-1/x=0` multiply by x
Now the second solution:
`x-1/x=3` multiply by x
`x^2-3x-1=0` use quadratic formula
There are four solutions to the original equation: