How many integer x between 1 to 10000000 will satisfy the equation given below sqrt(x)+sqrt(sqrt(x)

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21 Mar 2012 1 to 10000000

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

Correct Option: 2 Best Solution (0)