what is the sum of the digits of the integers solution to the square root of 14+the square root of27minuse?

Question

what is the sum of the digits of the integers solution to the square root of 14+the square root of 27 minus the square root of x+1 equal 4?

Answer 1

√14 + √27 - √(x + 1) = 4
One interpretation is
3 + 5 - √(x + 1) = 4
√(x + 1) = 4
x + 1 = 16
x = 17
sum-of-digits = 8

Another interpretation:
√(x + 1) = √14 + √27 - 4
x + 1 = 14 + 2√(14*27) + 27 - 8√14 - 8√27 + 16
x = 56 + 6√42 - 8√14 - 24√3
x = 23.38197
int(x) = 23
sum-of-digits = 5

Answer 2

0

there are no integer solutions????