Question

已知ax＋by=7 ax^2+by^2=49ax^3+by^3=133ax^4+by^4=406,求1995（x+y）+

Answer 1

tt=pt+q (x,y)是两根 F(n)=ax^n+by^n F(n+2)=pF(n+1)+qF(n) 133=49p+7q 406=133p+49q p=2.5 q=1.5 所以 2F(n+2)=5F(n+1)+3F(n) 2tt－5t－3＝0 (2t+1)(t-3)=0 x＋y=5／2 xy＝－3／2 x=3 y=-1/2 3a-1/2b=7，9a+b/4=49 a=5,b=16 所以a=5,b=16,x=3,y=-1/2