ax+by=7 ax2+by2=49 ax3+by3=133 ax4+by4=406
问题描述：
ax+by=7 ax2+by2=49 ax3+by3=133 ax4+by4=406
答
7(x+y)=(ax+by)(x+y)=ax²+(a+b)xy+by²=49+(a+b)xy
得7(x+y)=49+(a+b)xy
49(x+y)=(ax²+by²)(x+y)=ax³+(ax+by)xy+by³=133+7xy
得49(x+y)=133+7xy
133(x+y)=(ax³+by³)(x+y)=ax^4+（ax²+by²)xy+by^4=406+149xy
得133(x+y)=406+49xy
由以上三个方程解得x+y=5/2,xy=-3/2,a+b=21
得所求=4832