5X的方+4X-2=0

题目

5X的方+4X-2=0
9999X的方+2X-1=0
,已知X的方+X-1=0,则X的三次方+2X的方+2005=?
(m^2-1)x^2+mx+1/4=0

答案

5X^2+4X-2=0
X^2+4/5X-2/5=0
X^2+4/5X+4/25-2/5-4/25=0
(X+2/5)^2-14/25=0
(X+2/5-√14/5)(X+2/5+√14/5)=0
X=√14/5-2/5或X=-√14/5-2/5
9999X^2+2X-1=0
(101X-1)(99X+1)=0
X=1/101或X=-1/99
X的方+X-1=0,则X的三次方+2X的方+2005=?
X^2+X=1
X^3+X^2+X^2+2005
=X(X^2+X)+X^2+2005
=X^2+X+2005
=1+2005
=2006