F(x) = x^4-360x^2+400

F(x) = (x^2+20)^2 - 400x^2

F(x) = (x^2-20x+20)(x^2+20x+20) = Prime Number

Since the value of second factor is always positive and greater than 1 therefore, 1st factor has

to be equals to 1.

x^2-20x+20 = 1

x^2-20x+19= 0

On solving,

x = 1, 19.

Putting back the values in the original equation we get f(x) = 41 and f(x) = 761.

So, the sum will be 41+761 = 802