a^2+a+1=0,求a^4+2a^3-3a^2-4a+3的值
问题描述:
a^2+a+1=0,求a^4+2a^3-3a^2-4a+3的值
答
∵a²+a+1=0a⁴+2a³-3a²-4a+3=a²(a²+a+1)+a³-4a²-4a+3=a³-4a²-4a+3=a(a²+a+1)-5a²-5a+3=-5(a²+a-3/5)=-5(a²+a+1-8/5)=8