Question

已知：a 2 +4a+1=0，且 a 4 +m a 2 +1 2 a 3 +m a 2 +2a =3，则m的值为______

已知：a 2 +4a+1=0，且 a 4 +m a 2 +1 2 a 3 +m a 2 +2a =3，则m的值为______．

Answer 1

∵a 2 +4a+1=0，∴a 2 =-4a-1， a 4 + ma 2 +1 2 a 3 + ma 2 +2a = (-4a-1 ) 2 + ma 2 +1 2a(-4a-1)+ ma 2 +2a = (16+ m)a 2 +8a+2 (m-8 )a 2 = (16+m)(-4a-1)+8a+2 (m-8)(-4a-1) = (-56-4m)a-14-m (-4m+32)a-m+8 =3 即（-56-4m）a-14-m=（-12m+96）a-3m+24， ∴-56-4m=-12m+96，-14-m=-3m+24， 解得m=19． 故答案为19．