Question

已知a=2/根号3-1 求1/2a的立方-a的平方-a+2的值

Answer 1

a=2/(√3-1)=(√3+1)(√3-1)/(√3-1)=√3+1

1/2a^3-a^2-a+2

=1/2a^2*a-a^2-a+2

=1/2(√3+1)^2*(√3+1)-(√3+1)^2-(√3+1)+2

=1/2(4+2√3)(√3+1)-(4+2√3)-√3+1

=1/2(6√3+10)-4-2√3-√3+1

=3√3+5-4-2√3-√3+1

=2