Question

m*m－m－1＝0 求m

已知m的平方-m-1=0，求代数式m的立方-2m+1的值

Answer 1

m²-m-1=0
m²-m+1/4-1/4-1=0
(m-1/2)²-5/4=0
(m-1/2-√5/2)(m-1/2+√5/2)=0
m=1/2+√5/2或m=1/2-√5/2

m²-m-1=0
m²-m=1

m³-2m+1
=m³-m²+m²-2m+1
=m(m²-m)+m²-2m+1
=m+m²-2m+1
=m²-m+1
=1+1
=2

Answer 2

m²-m=1
m²-m+1/4=1+1/4
(m-1/2)²=5/4
m-1/2=±√5/2
m=(1-√5)/2，m=(1+√5)/2