Question

关于一道二次根式的数学题

先化简再求值：2(a+√3（根号三）)（a-√3）-a(a-6)+6,其中a=√2 - 1

Answer 1

解：2(a+√3)(a-√3)-a(a-6)+6
=2(a^2-3)-a^2+6a+6
=2a^2-6-a^2+6a+6
=a^2+6a
=a(a+6)
当a=√2 -1时，a(a+6)=(√2 -1)(√2 -1+6)=4√2-3

Answer 2

2(a+√3)(a-√3)-a(a-6)+6
=2(a^2-3)-a^2+6a+6
=a^2+6a
将a=√2 - 1带入得
原式=4√2-3

Answer 3

2(a+√3（根号三）)（a-√3）-a(a-6)+6=2(a^2-3)-a^2+6a+6=a^2+6a
=(√2-1)^2+6(√2-1)=3-2√2+1+6√2-6=4√2-2