已知:m^2-m-3=0,求m^3+999m^2-1003m-992的值

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已知:m^2-m-3=0,求m^3+999m^2-1003m-992的值

已知:m^2-m-3=0,求m^3+999m^2-1003m-992的值
已知:m^2-m-3=0,求m^3+999m^2-1003m-992的值

已知:m^2-m-3=0,求m^3+999m^2-1003m-992的值
m^2=m+3
假设m^3+999m^2-1003m-992=a
m(m^2+999m-1003)-992
=m(m+3+999m-1003)-992
=m(1000m-1000)-992
=1000m^2-1000m+3000-2008=
=1000(m^2-m-3)+2008=a
所以a=2008

m^2-m-3=0
m^2-m=3
m^3+999m^2-1003m-992
=m^3-m^2+1000m^2-1003m-992
=m(m^2-m)+1000m^2-1003m-992
=3m+1000m^2-1003m-992
=1000m^2-1000m-992
=1000(m^2-m)-992
=3*1000-992
=3000-992
=2008