已知ax+by=7,ax^2+by^2=49,ax^3+by^3=133,ax^4+by^4=406.求：2001（x+y）+6xy-17/2（a+b）的值
问题描述：
已知ax+by=7,ax^2+by^2=49,ax^3+by^3=133,ax^4+by^4=406.求：2001（x+y）+6xy-17/2（a+b）的值
答
设x+y = mxy = na + b = k(x+y)(ax+by) = ax^2+by^2+(a+b)xy =>7m = 49+kn (1)(x+y)(ax^2+by^2) = ax^3+by^3+(ax+by)xy => 49m = 133 + 7n (2)(x+y)(ax^3+by^3) = ax^4+by^4+(ax^2+by^2)xy => 133m = 406 + 49n (3)...