ironone
幼苗
共回答了18个问题采纳率:94.4% 举报
ax^2=49-by^2, by^2=49-ax^2
=>ax^3=49x-bxy^2, by^3=49y-ax^2y
相加得
ax^3+by^3=49(x+y)-xy(ax+by)=133
=>49(x+y)-7xy=133
7(x+y)-xy=19 (1)
同理 ax^3=133-by^3,by^3=133-ax^3
=>ax^4=133x-bxy^3,by^4=133y-ax^3y
相加得
406=ax^4+by^4=133(x+y)-xy(ax^2+by^2)
=>133(x+y)-49xy=406
19(x+y)-7xy=58 (2)
由(1)(2)联立,设x+y=M,xy=N
得 7M-N=19
19M-7N=58,解得 M=2.5,N=-1.5
=> x+y=2.5,xy=-1.5
ax=7-by,by=7-ax
=>ax2=7x-bxy,by2=7y-axy
相加得49=ax2+by2=7(x+y)-xy(a+b)
=> 1.5(a+b)=49-7×2.5
=> a+b=21
所以,原式=2005*2.5+6*(-1.5)-17/2*21=4825
1年前
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