Given a 2-3a + 1 = 0, find the value of (a + 1 / a 2-2) 1 / 2 I translate it in Chinese Is a square - 3A + 1 = 0 find the root sign [(a + 1) divided by (a square - 2)]

Given a 2-3a + 1 = 0, find the value of (a + 1 / a 2-2) 1 / 2 I translate it in Chinese Is a square - 3A + 1 = 0 find the root sign [(a + 1) divided by (a square - 2)]

If a & sup2; - 3A + 1 = 0a-3 + (1 / a) = 0A + 2 + (1 / a) = 5a-2 + (1 / a) = 1, then (a + 2 + (1 / a)) / (A-2 + (1 / a)) = 5 times a (A & sup2; + 2A + 1) / (A & sup2; - 2A + 1) = 5 (a + 1) & sup2; / (A-1) & sup2; = 5 radical [(a + 1) / (A-1)] = radical [(a + 1) / (A & sup2; - 2)] = radical

Given a ^ 2 + A-1 = 0, find the value of 3A ^ 3-6a + 3

a^2+a-1=0,
a^2+a+1=2
Multiply both sides by (A-1)
(a-1)(a^2+a+1)=2(a-1)
a^3-1=2a-2
a^3-2a=-1
3a^3-6a+3
=3(a^3-2a)+3
=3×(-1)+3
=0

Let a be a real number and let A3 + 3a2 + 3A + 2 = 0, then the value of (a + 1) 1996 + (a + 1) 1997 + (a + 1) 1998 is______ ．

Solution 1: ∵ A3 + 3a2 + 3A + 2 = 0 ∵ (a + 1) 3 + 1 = 0 ∵ (a + 1) 3 = - 1 ∵ a + 1 = - 1 ∵ 1996 + (a + 1) 1997 + (a + 1) 1998 = 1 + (- 1) + 1 = 1. Solution 2: ∵ (a + 1) 2 = A2 + 2A + 1, that is, a (a + 1) 2 = A3 + 2A2 + A, the solution is: A3 = a (a + 1) 2-2a2-a, substituting into A3 + 3a2 + 3A +