It is known that the minimum value of function f (x) = (2 ^ x-a) ^ 2 + (2 ^ - x-a) ^ 2 is 8, and there is a value range of real number a

It is known that the minimum value of function f (x) = (2 ^ x-a) ^ 2 + (2 ^ - x-a) ^ 2 is 8, and there is a value range of real number a

If f (x) = (2 ^ x-a) ^ 2 + (2 ^ (- x) - a) ^ 2 = 4 ^ x + A ^ 2-2a * 2 ^ x + 4 ^ (- x) + A ^ 2-2a * 2 ^ (- x) = (2 ^ x + 2 ^ (- x)) ^ 2-2a (2 ^ x + 2 ^ (- x)) + 2A ^ 2-2, let t = 2 ^ x + 2 ^ (- x) (t ≥ 2), then f (T) = T ^ 2-2at + 2A ^ 2-2 = (T-A) ^ 2 + A ^ 2-2

It is known that the quadratic function f (x) = ax ^ 2 + BX + C (a, B, C ∈ R) satisfies f (1) = 1, f (- 1) = 0 and f (x) ≥ x for any real number X
If x ∈ (0,2), f (x)

f(1)=a+b+c=1,
f(-1)=a-b+c=0.
By subtracting, we get 2B = 1, B = 1 / 2
∴a+c=1/2.(1)
For any real number x, f (x) > = x,
ax^2-x/2+c>=0,
a> 0, and 1 / 4-4ac