∵X²-X-1=0
(X-1/2)²=5/4
∴X=（1±√5）/2
當(dāng)a=(1+√5)/2,b=(1-√5）/2時,
代數(shù)式a³+3b=1/8(1+√5)(1+√5)(1+√5)+3(1-√5)/2
=1/4(3+√5)(1+√5)+3(1-√5)/2
=2+√5+3/2-√5/2
=(7+√5)/2
當(dāng)a=(1-√5)/2,b=(1+√5）/2時,
代數(shù)式a³+3b=1/8(1-√5)(1-√5)(1-√5)+3(1+√5)/2
=1/4(3-√5)(1-√5)+3(1+√5)/2
=2-√5+3/2+√5/2
=(7-√5)/2