Question

急！已知X的平方-X+1分之X=6,求X四次方+X平方+1分之X的平方的值 ！

已知X的平方-X+1分之X=6,求X四次方+X平方+1分之X的平方的值 ！

Answer 1

取倒数 X分之（ X的平方-X+1）=6分之1
X+X分之1=6分之7
两边平方
X平方+2+X平方分之1=36分之49
X平方+1+X平方分之1=36分之13
左边同分取倒数
X四次方+X平方+1分之X的平方=13分之36

Answer 2

x/(x^2-x+1)=6
1/(x-1+1/x)=6
x-1+1/x=1/6
x+1/x=1+1/6=7/6
(x+1/x)^2=49/36
x^2+1/x^2+2=49/36
x^2+1/x^2=49/36-2=-23/36

x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/{(x^2+1/x^2)+1}
=1/(1-23/36)
=36/(36-23)
=36/13

Answer 3

解：由x/(x^2-x+1)=6，得
x=6x^2-6x+6
13x=6x^2+6x+6
x/(x^2+x+1)=6/13
则
x^2/(x^4+x^2+1)=x^2/[(x^2-x+1)(x^2+x+1)]
=x/(x^2-x+1)*x/(x^2+x+1)
=6*6/13
=36/13

Answer 4

由已知条件得x+1/x=7/6;
求解式=1/[(x+1/x)² -1]=36/13.

Answer 5

b的平方-4ac<0此式无解，