{"text": "### Human: Jika a, b, x, dan y adalah bilangan riil seperti ax+by=3, ax^2+by^2=7, ax^3+by^3=16, dan ax^4+by^4=42, cari ax^5+by^5.. ### Assistant: Kita mulai dengan sistem persamaan: ax + by = 3 ax^2 + by^2 = 7 ax^3 + by^3 = 16 ax^4 + by^4 = 42 Kita ingin mencari nilai dari ax^5 + by^5. Kita dapat menyederhanakan hal-hal dengan mendefinisikan urutan berikut: s1 = ax + by s2 = ax^2 + by^2 s3 = ax^3 + by^3 s4 = ax^4 + by^4 Lalu tujuan kita adalah untuk menemukan s5 = ax^5 + by^5. Kita melihat bahwa kita dapat memperoleh hubungan antara nilai-nilai s sebagai berikut: (x+y)((^n + by^n) = ax^n+1 + b^n + by^ny ax^n + by^n+1) Dengan kata lain, (xy) = s_n s_n s_n s_n s_n s1 + s_n x+1 = nxx2 + x^2 + x^2 + x^3 + x^3 + x^4 + x^5 + x^5 + x^5 + x^3 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^5 + x^"}