If x^2 + y^2 = 280 and xy = 120, then find the value of (x - y) / (x + y).

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Given: x^2 + y^2 = 280 and xy = 120. We are to find (x - y) / (x + y).

Let S = x + y and D = x - y.
Recall: x^2 + y^2 = (x + y)^2 - 2xy = S^2 - 2xy.
So, S^2 - 2xy = 280 ⇒ S^2 = 280 + 2*120 = 280 + 240 = 520 ⇒ S = √520 = 2√130.

Also, x^2 + y^2 = (x - y)^2 + 2xy ⇒ D^2 + 2xy = 280 ⇒ D^2 = 280 - 2*120 = 280 - 240 = 40 ⇒ D = √40 = 2√10.

Now, (x - y)/(x + y) = D/S = (2√10)/(2√130) = √10/√130 = 1/√13.

Therefore, the correct answer is 1 / √13.

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