已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值

已知ax+by=7，ax²+by²=49，ax³+by³=133，ax⁴+by⁴=406，求2003(x+y)+6xy-(7/2)(a+b)的值
(ax+by)(x+y)=ax²+by²+(a+b)xy=49+(a+b)xy=7(x+y)
即有(a+b)xy-7(x+y)=-49.............(1)
(ax²+by²)(x+y)=ax³+by³+xy(ax+by)=133+7xy=49(x+y)
即有7xy-49(x+y)=-133..............(2)
(ax³+by³)(x+y)=ax⁴+by⁴+xy(ax²+by²)=406+49xy=133(x+y)
即有49xy-133(x+y)=-406...........(3)
7×(2)-(3)得 x+y=525/210=105/42=5/2；7xy-49(5/2)=-133，故xy=-3/2；
将xy和x+y之值代入(1)式即得a+b=21
于是2003(x+y)+6xy-(7/2)(a+b)=2003×(5/2)+6×(-3/2)-(7/2)×21=(10015-18-147)/2=4925

ax + by = 7,两边同时乘以x + y,由ax2+by2=49,得到49 + （a + b）xy = 7(x + y) ***ax2+by2=49,两边同时乘以x + y,由ax3+by3=133,得到19 + xy = 7(x + y) *ax3+by3=133,两边同时乘以x + y,由ax4+by4=406,得到58 + 7...