Question

(1)若Aˇ2-6AB+9Bˇ2-1.5A+4.5B+M/2是完全平方式,则M=?

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