已知f(x)=x^8-2x^7-2x^5-2x^3-2x,则log2 f(根号2+1）=
问题描述：
已知f(x)=x^8-2x^7-2x^5-2x^3-2x,则log2 f(根号2+1）=
答
设 a=√2+1
因为(√2+1)*(√2-1)=(√2+1)*(√2+1-2)=1
即a(a-2)=1
a^8-2a^7-2a^5-2a^3-2a
=a^7(a-2)-2a^5-2a^3-2a
=a^6*a(a-2)-2a^5-2a^3-2a
=a^6-2a^5-2a^3-2a
=a^5*(a-2)-2a^3-2a
=a^4-2a^3-2a
=a^3(a-2)-2a
=a^2-2a
=a(a-2)=1
log2 f(根号2+1）=log2(1)=0