已知a2-a-1=0,且2a4−3xa2+2a3+2xa2−a=−93/112,则x=_.
问题描述:
已知a2-a-1=0,且
=−2a4−3xa2+2
a3+2xa2−a
,则x=______. 93 112
答
由题意可得a2-a-1=0
a2=a+1
a4=(a2)2=(a+1)2=a2+2a+1=a+1+2a+1=3a+2
a3=a•a2=a(a+1)=a2+a=a+1+a=2a+1
=-2a4−3a2x+2
a3+2a2x−a
93 112
=-6a+4−3a2x+2 2a+1+2a2x−a
93 112
672a+672-336xa2=-93a-93-186xa2
150xa2=765a+765=765(a+1)=765a2
150x=765
x=5.1.