SOLUTION: Solve y=x+1/x with 0<x<=1 for x in terms of y.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve y=x+1/x with 0<x<=1 for x in terms of y.      Log On


   

Question 344883: Solve y=x+1/x with 0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for x. Since x cannot be zero, we can go ahead and multiply both sides of the equation by x. This will eliminate the fraction:
xy+=+x%5E2+%2B+1
Next we'll get one side equal to zero (because we are about to use the Quadratic Formula) by subtracting xy from each side:
0+=+x%5E2+-xy+%2B+1
Because multiplication is commutative and because it may make the next step clearer, I'm going to rewrite xy as yx:
0+=+x%5E2+-yx+%2B+1
Now we will use the Quadratic formula with a = 1, c = 1 and b = -y! This is an unusual yet still valid way to use the Quadratic Formula.
x+=+%28-%28-y%29+%2B-+sqrt%28%28-y%29%5E2+-+4%281%29%281%29%29%29%2F2%281%29
which simplifies as follows:
x+=+%28-%28-y%29+%2B-+sqrt%28y%5E2+-+4%281%29%281%29%29%29%2F2%281%29
x+=+%28y+%2B-+sqrt%28y%5E2+-+4%29%29%2F2
This equation has x solved for in terms of y.