求a分之2,加a平方分之2,加a三次方分之1的值,a=4的三次方根+2的三次方根+1的三次方根

Question

求a分之2,加a平方分之2,加a三次方分之1的值,a=4的三次方根+2的三次方根+1的三次方根

Answer 1

a=4^(1/3)+2^(1/3)+1^(1/3)=t^2+t+1 t=2^(1/3) t^3-1=2-1=1
2/a+2/a^2+1/a^3=2(t-1)/(t^3-1)+2(t-1)^2/(t^3-1)^2+(t-1)^3/(t^3-1)^3
=2(t-1)+2(t-1)^2+(t-1)^3
=(t-1)(2+2t-2+t^2+1-2t)
=(t-1)(t^2+1)
=t^3-1-t^2+t
=1-4^(1/3)+2^(1/3)