SOLUTION: Leave x in terms of y if... t^2-4x^2t+4x^4=0 and t^2-1 / y = t-1 / √y I am not sure how to approach this question. Could you please help? Thank you.

Algebra ->  Equations -> SOLUTION: Leave x in terms of y if... t^2-4x^2t+4x^4=0 and t^2-1 / y = t-1 / √y I am not sure how to approach this question. Could you please help? Thank you.       Log On


   

Question 805556: Leave x in terms of y if...
t^2-4x^2t+4x^4=0 and t^2-1 / y = t-1 / √y

I am not sure how to approach this question.
Could you please help?
Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Leave x in terms of y if...
t^2-4x^2t+4x^4=0
Factors to
(t-2x^2)(t-2x^2) = 0
t = 2x^2
:
and
%28t%5E2-1%29%2Fy = %28t-1%29%2Fsqrt%28y%29
cross multiply
sqrt%28y%29(t^2-1) = y(t-1)
sqrt%28y%29(t-1)(t+1) = y(t-1)
divide both sides by (t-1)
sqrt%28y%29(t+1) = y
t + 1 = y%2Fsqrt%28y%29
t + 1 = sqrt%28y%29
Replace t with 2x^2 from the 1st equation
2x^2 + 1 = sqrt%28y%29
square both sides
y = (2x^2+1)^2
FOIL
y = 4x^4 + 4x^2 + 1