SOLUTION: If x > 0 and y> 0 and x^2 - y^2 = 2xy, find the exact value of x/y

Question 1119231: If x > 0 and y> 0 and x^2 - y^2 = 2xy, find the exact value of x/y
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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In your original equation 

x^2 - y^2 = 2xy

divide both sides by y^2.  You will get


 = ,   or


 = 0.


In the last equation, introduce new variable t = .  Then the equation takes the form

t^2 - 2t - 1 = 0.


Apply the quadratic formula:

 =  =  = .


Since t = x/y  and  x > 0, y > 0,  only positive root  t =    works and gives the 


Answer.   = .

Solved.

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