math help please!!?

x^2-y^2=2xy and if x and y are both positive, find the ratio :

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if you could help and show your work i would really appreciate it!!

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

You want to find x / y.

Therefore put x / y = k, so that x = yk, and you can then solve for k.

x^2 – y^2 = 2xy

becomes

y^2k^2 – y^2 = 2y^2k

y^2k^2 – y^2 – 2y^2k = 0

y^2(k^2 – 2k – 1) = 0

As y is positive, you can safely divide by y^2:

k^2 – 2k – 1 = 0

k = ( 2 +/- sqrt(4 + 4) ) / 2

= 1 +/- sqrt(4)sqrt(2) / 2

= 1 +/- sqrt(2).

As x and y are both positive, k must be positive, and therefore:

x / y = k = 1 + sqrt(2).

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