The pattern or the logic that is followed in this puzzle is:

(number1) : (number1)^2 +1 :: (number2) : (number2)^2+1

from the question, number1=4 and number 2 is 7, so applying the above pattern or formula, we get the following system:

(4) : (4)^2 + 1 :: (7) : (7)^ + 1

so, the value of ? is 7^2 +1 or 49+1 which is 50.

so, the missing number is 50.