Question

m²-m-1=0,则m的5次-5m-3的值为

Answer 1

您好：

m²-m-1=0
m²-1=m
(m²-1)²=m²
m^4-2m²+1=m²
m^4+1=3m²

m^5-5m-3
=m(m^4+1)-6m-3
=3m³-6m-3
=3m(m²-1)-3m-3
=3m²-3m-3
=3(m²-m-1)
=0

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Answer 2

m的5次-5m-3
=m^5-m^4-m^3+m^4-m^3-m^2+m^3-m^2-m+m^3+2m^2-4m-3
=m³(m²-m-1)+m²(m²-m-1)+m(m²-m-1)+m³+2m²-4m-3
=m³-m²-m+3m²-3m-3
=m(m²-m-1)+3(m²-m-1)
=0+0
=0

Answer 3

由 m^2-m-1=0，得 m^2 = m +1
m^5-5m-3
=mm^4-5m-3
=m(m+1)^2-5m-3
=m(m^2+2m+1)-5m-3
=m(m+1+2m+1)-5m-3
=m(3m+2)-5m-3
=3m^2+2m-5m-3
=3(m+1)-3m-3
=3m+3-3m-3
=0

Answer 4

解：由m²-m-1=0，得 m²=m+1 m²-m=1
原式=m(m²)²-5m-3=m(m+1)²-5m-3=m(m²+2m+1)-5m-3=m(m+1+2m+1)-5m-3
=3(m²-m-1)=0

Answer 5

解： m²-m-1=0
m²-1=m
(m²-1)²=m²
m^4-2m²+1=m²
m^4+1=3m²

m^5-5m-3
=m(m^4+1)-6m-3
=3m³-6m-3
=3m(m²-1)-3m-3
=3m²-3m-3
=3(m²-m-1)
=0

Answer 6

您好：

m²-m-1=0
m²-1=m
(m²-1)²=m²
m^4-2m²+1=m²
m^4+1=3m²

m^5-5m-3
=m(m^4+1)-6m-3
=3m³-6m-3
=3m(m²-1)-3m-3
=3m²-3m-3
=3(m²-m-1)
=0
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