实数a,b,x,满足ax+by=3,ax^2+by^2=7,ax^3+by^3=16,ax^4+by^4=42,ax^5+by^5=?

题目

实数a,b,x,满足ax+by=3,ax^2+by^2=7,ax^3+by^3=16,ax^4+by^4=42,ax^5+by^5=?

答案

因为ax2+by2=7 则ax2=7-by2,by2=7-ax2 ax3=7x-bxy2,by3=7y-ax2y ax3+by3=7(x+y)-xy(by+ax)=16 即7(x+y)-3xy=16 又因为ax3+by3=16 则ax3=16-by3,by3=16-ax3 ax4=16x-bxy3,by4=16y-ax3y ax4+by4=16(x+y)-xy(by2+ax2)=4...