- 求助p(x)如果p(x)=x^2+tx+s证明：p(x)*p(x
- 如果p(x)=x^2+tx+s
证明：p(x)*p(x+1)=p[p(x)+x]
多谢
- 如果 p(x)=x²+tx+s
证明：p(x)*p(x+1)=p[p(x)+x]
P(x)P(x+1) = p(x)[(x+1)²+t(x+1)+s]
= p(x)[x²+2x+1+tx+t+s]
= p(x)[p(x)+2x+(t+1)]
= p(x)²+2xp(x)+p(x)(t+1)
= p(x)²+2xp(x)+(x²+tx+s)(t+1)
= p(x)²+2xp(x)+x²(1+t)+(tx+s)(t+1)
= [p(x)+x]²+tx²+(t²x+ts)+(tx+s)
= [p(x)+x]²+t(x²+tx+s)+(tx+s)
= [p(x)+x]²+t[p(x)+x]+s
= p[p(x)+x]