若a=1/2-根号3,求3a2-12a+5的值 若a=1/根号2 +1 求a3+a2-3a-1的值
问题描述：
若a=1/2-根号3,求3a2-12a+5的值 若a=1/根号2 +1 求a3+a2-3a-1的值
答
a=1/(2-√3)=(2+√3)/[(2-√3)(2+√3)]=2+√3
3a²-12a+5
=3a²-12a+12-7
=3(a-2)²-7
=3(2+√3-2)²-7
=3(√3)²-7
=9-7
=2
a=1/(√2+1)=(√2-1)/[(√2+1)(√2-1)]=√2-1
a³+a²-3a-1
=a²(a+1)-3(a+1)+2
=(√2-1)²(√2-1+1)-3(√2-1+1)+2
=(3-2√2)√2 -3√2 +2
=3√2-4-3√2+2
=-2