Question

find integer solution for x \[\huge x^2+2=\sqrt{2^x}+4\log_2x \]

Answer 1

@hartnn ??? @Callisto ??

Answer 2

@whpalmer4 ??? @timo86m ???

Answer 3

@Directrix ??? @Hero ??

Answer 4

@AccessDenied ???

Answer 5

@zzr0ck3r ??

Answer 6

wait up

Answer 7

just from looking at the equation
2 is a solution

Answer 8

yea, i look at that was well haha

Answer 9

that why i paused for a second

Answer 10

what class is this for? @deena123 ?

Answer 11

NOTE: for any integer value of x L.H.S will always be integer
when x>=4
LHS will never be a multiple of 4. ( you can easily prove this)
now, in the case of R.H.S
either RHS will be integer or it will not be an integer.
if it is not an integer then that value of x will not be the solution
AND if it is integer then it must be the multiple of 4.(this is also not difficult to prove)
BUT LHS will never be a multiple of 4 so this value of x will also not be the solution.
THUS, no solution of x for x>=4
Now,
x cannot be less than or equal to 0 and x=1,3 are also not the solution.
The only solution of x is 2.

Answer 12

very cool

Answer 13

I hope I can come up with that some day:)

Answer 14

why did u take multiple of 4 only??