{"text": "### Human: Carilah nilai minimum dari (x^2) / ((y - 1) + (y^2) / ((x - 1) untuk bilangan riil x > 1 dan y > 1.. ### Assistant: Mari kita katakan a = x - 1 dan b = y - 1. Maka x = a + 1 dan y = b + 1, jadi (x^2) /(y - 1) + (y^2) /(x - 1) = ((a + 1) ^2) /b + ((b + 1) ^2) /a = (a^2 + 2a + 1) /b + (b^2 + 2b + 1) /a = 2 (a/b + b/a) + (a^2) /b + 1/b + (b^2) /a + 1/a. Dengan AM-GM, kita memiliki: a/b + b/a \u2265 2 sqrt (a/b*b/a) = 2 dan (a^2) /b + 1/b + (b^2) /a + 1/a \u2265 4 ((a2) ^*b*1/b*2) = 1 x = 2 x = 2 x = 2 x = 8 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 8 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 8 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 8 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 8 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 x = 2 = 2 x = 2 x = 2 = 2 x = 2 = 2 x = 2 = 2 = 2 x = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 ="}