已知a=3√4+3√2+3√1,（3是根指数）那么,3/a+3/a^2+1/a^3的值为.

Question

已知a=3√4+3√2+3√1,（3是根指数）那么,3/a+3/a^2+1/a^3的值为______.

Answer 1

令x=3√2
a=x²+x+1
(x-1)(x²+x+1)=x³-1=2-1=1
1/a=x-1
原式=3(x-1)+3(x-1)²+(x-1)³
=3x-3+3x²-6x+3+x³-3x²+3x-1
=x³-1
=1