完全平方公式的题初一的若m与他的倒数的和为3,求m的平方与其倒数的和,及m的四次方与其倒数的和.（2a+3b-c+1)(

m+1/m=3
两边平方,且中间一项=2*m*1/m=2
所以m^2+2+1/m^2=9
m^2+1/m^2=7
m^2+1/m^2=7
两边平方
m^4+2+1/m^4=49
m^4+1/m^4=47
(2a+3b-c+1)(2a+3b-c-1)
=[(2a+3b-c)+1][(2a+3b-c)-1]
=(2a+3b-c)^2-1^2
=[(2a+3b)-c]^2-1
=(2a+3b)^2-2c(2a+3b)+c^2-1
=4a^2+9b^2+c^2+12ab-4ac-6bc-1
(y-3)^2-2(y+2)(y-2)
=(y^2-6y+9)-2(y^2-4)
=y^2-6y+9-2y^2+8
=-y^2-6y+17

m的平方与其倒数的和=（m+1/m)^2-2=9-2=7
m的四次方与其倒数的和=(m^2+1/m^2)^2-2=47
（2a+3b-c+1)(2a+3b-c-1)=(2a+3b-c)^2-1
(y-3)^2-2(y+2)(y-2)
=-y^2-6y+17