完全平方公式的题初一的
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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)(2a+3b-c-1)
(y-3)^2-2(y+2)(y-2)
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)(2a+3b-c-1)
(y-3)^2-2(y+2)(y-2)
![完全平方公式的题初一的](/uploads/image/z/15025017-57-7.jpg?t=%E5%AE%8C%E5%85%A8%E5%B9%B3%E6%96%B9%E5%85%AC%E5%BC%8F%E7%9A%84%E9%A2%98%E5%88%9D%E4%B8%80%E7%9A%84)
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
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