Re: algebra problem
Set x=a^(1/2). Then your equation becomes
x^4 - x^3 + x^2 - 1=0
which can be factored as
(x - 1)(x^3 + x + 1) = 0
Therefore, you have a solution x=1, which means a=1.
As for x^3 + x + 1 = 0. Algebra tells you that any rational solution has to be a factor of the const term which is 1 in this case. Therefore, you have only two choice, 1 or -1. Direct substitutions show that none of them is the solution of x^3 + x + 1 = 0. Thus, you are left out with only irrational solutions.
Further analysis can be done as follows. Set
f(x)=x^3 + x + 1
Take derivative
f'(x)=3*x^2+1 >0
which means that f(x) is an increasing function and, therefore, has only one real solution. The other two are complex solutions.