如果关于字母X的二次多项式-3x^2+mx+nx^2-x+3的值与x的取值无关,求代数式-m^2-(1/2)[3n^2-2(m^2-n^2)]+6的

Question

如果关于字母X的二次多项式-3x^2+mx+nx^2-x+3的值与x的取值无关,求代数式-m^2-(1/2)[3n^2-2(m^2-n^2)]+6的

Answer 1

-3x^2+mx+nx^2-x+3的值与x的取值无关
（-3+n）x²+（m-1）x+3
-3+n=0 m-1=0
n=3 m=1
-m^2-(1/2)[3n^2-2(m^2-n^2)]+6
=-m^2-(1/2)[3n^2-2m^2+2n^2)]+6
=-m^2-(1/2)（5n^2-2m^2)+6
=-m^2-5n^2/2+m^2+6
=-5n^2/2+6 其中n=3
=-5×3²/2+6
=-22.5+6
=-16.5