一道题，简单～

<>是根号,/除号
a=4/<5>+1
a=4*(<5>-1)/(<5>-1)*(<5>+1)
a=<5>-1
1/2a^3-a^2-2a-1
=1/2a^3+1/2-(a^2+2a+1)-1/2
=1/2(a^3+1)-(a+1)^2-1/2
=1/2(a+1)*(a^2-a+1)-(<5>-1+1)^2-1/2
=1/2<5>*((5-2<5>+1)-<5>+1+1)-5-1/2
=1/2<5>*(8-3<5>)-11/2
=4<5>-15/2-11/2
=4<5>-13

∵a=4/(√5+1)分母有理化(分子分母同乘以√5-1)得:
a=√5-1
∴1/2a^3-a^2-2a-1
=1/2a^3-(a^2+2a+1)
=1/2a^3-(a+1)^2
=1/2(√5-1)^3-(√5-1+1)^2
=1/2(8√5-16)-(√5)^2
=4√5-8-5
=4√5-13.

化简a得：根号5-1
原式=1/2a^3-(a+1)^2
=1/2a^3-(根号5-1+1)^2
=1/2a^3-5
=1/2a^2*a-5
=1/2(根号5-1)^2*(根号5-1)-5
=1/2(6-2倍根号5)*（根号5-1）-5
=（3-根号5）*（根号5-1）-5
=四倍根号5-8-5
=四倍根号5-13
或
∵a=4/(√5+1)分母有理化(分子分母同乘以√5-1)得:
a=√5-1
∴1/2a^3-a^2-2a-1
=1/2a^3-(a^2+2a+1)
=1/2a^3-(a+1)^2
=1/2(√5-1)^3-(√5-1+1)^2
=1/2(8√5-16)-(√5)^2