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...