(1)若Aˇ2-6AB+9Bˇ2-1.5A+4.5B+M/2是完全平方式,则M=?(2)已知X/(Xˇ2+1)=0.1,求Xˇ2+1/(Xˇ2)的值.(3)若(Xˇ3+MX+N)(Xˇ2-2X+5)展开后,不含Xˇ3和Xˇ2项,求M,N的值.

Question

(1)若Aˇ2-6AB+9Bˇ2-1.5A+4.5B+M/2是完全平方式,则M=?
(2)已知X/(Xˇ2+1)=0.1,求Xˇ2+1/(Xˇ2)的值.
(3)若(Xˇ3+MX+N)(Xˇ2-2X+5)展开后,不含Xˇ3和Xˇ2项,求M,N的值.

Answer 1

(1)
细看多项式
设A^2-6AB+9B^2-1.5A+4.5B+M/2=(A-3B+X)^2=A^2-6AB+9B^2+2X*A-6X*B+X^2
2X=-1.5 -6X=4.5 X^2=M/2 X=-3/4 M=9/8
(2)
可知X^2+1=10X
X^2+1/(X^2)=(X^4+1)/(X^2)
=[(X^2+1)^2-2X^2]/(X^2)=(100X^2-2X^2)/(X^2)=98
(3)
(X^3+MX+N)(X^2-2X+5)展开后
X^3项的系数为M+5
X^2项的系数为N-2M
所以M+5=0 N-2M=0
M=-5 N=-10