How many integer x between 1 to 10000000 will satisfy the equation given below
sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrt(x)))+sqrt(sqrt(sqrt(sqrt(x))))=A
here A is an integral positive number
OPtion
1) 1
2) 2
3) 3
4) 128
5) 512
6) 4096
7) 12456
8) 65536
9) more that 100000
10) not possible to calculate
Solution
since last term contains 4 sqrt so 16 powers are necessary to get an integral value
so answers will be 1^16, 2^16, 3^16 ....
but 3^16 is greater than 10000000 hence it will be a non valid answer
so 2 values of x are possible
As a toddler when I looked at my fingers and wondered,
you helped me to count numbers.
As a kid when I looked at stars with awe,
you helped me and told that's infinity.
As a teen when my confused mind often went blank,
you told that's zero and eventually
vinotha
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.