ax+bx=3,ax^2+by^2=7,ax^3+by^3=16,ax^4+by^4=42,求ax^5+bx^5.
问题描述：
ax+bx=3,ax^2+by^2=7,ax^3+by^3=16,ax^4+by^4=42,求ax^5+bx^5.
答
ax^2+by^2=7(ax^2 + by^2)(x+y) = 7(x+y)ax^3 +by^3 + ax^2y+bxy^2 = 7(x+y)ax^3 + by^3 + xy(ax+by) = 7(x+y)以 ax+by = 3,ax^3 +by^3 = 16 代入上式16 + 3xy = 7(x+y)ax^3+by^3=16(ax^3 + by^3)(x+y) = 16(x+y)ax^...