Given x 2-4x + 1 = 0, find the value of x 2 + X-2 The square of X is the sum of the square of X and the minus second power of X

Given x 2-4x + 1 = 0, find the value of x 2 + X-2 The square of X is the sum of the square of X and the minus second power of X

X ^ 2-4x + 1 = 0 so x ^ 2 + 1 = 4x so x + 1 / x = 4
Then x ^ 2 + x ^ - 2 = (x + 1 / x) ^ 2 - 2 = 4 ^ 2 - 2 = 14

It is known that f (x) = 4x / (3x2 + 3) (x belongs to (0,2)), G (x) = (1 / 2) x2-inx-a
(1) Find the range of F (x); (2) if x belongs to [1,2] such that G (x) = 0, find the range of a; (3) for all X1 belong to (0,2), there is always x2 belonging to [1,2] such that f (x1) = g (x2), find the range of A

（1）
f(x)=4x/(3x2+3)
f'(x)=(12x^2+12-4x*6x)/(3x^2+3)^2
=-12(x+1)(x-1)/(3x^2+3)^2
0