x> 0. Let say internal x^1/2 and external (x*x^1/2)^1/2 >>>>> (x^1+1/2)^1/2 >>>> (x^3/2)^1/2 = 8 Let take log on base 2 >>>> 1/2*log_2 of x^3/2 = 3 >>>> log_2 of x^3/2 = 6 3/2 *log_2 x = 6. >>>>> log_2 of x = 4 and x=2^4 means x= 16 Verify - internal 16^1/2 =4 and external (16*4)^1/2>>>> (16^1/2) * (4 ^1/2) = 2*4=8.
Lovely.
x> 0. Let say internal x^1/2 and external (x*x^1/2)^1/2 >>>>> (x^1+1/2)^1/2 >>>>
(x^3/2)^1/2 = 8 Let take log on base 2 >>>> 1/2*log_2 of x^3/2 = 3 >>>> log_2 of x^3/2 = 6
3/2 *log_2 x = 6. >>>>> log_2 of x = 4 and x=2^4 means x= 16
Verify - internal 16^1/2 =4 and external (16*4)^1/2>>>> (16^1/2) * (4 ^1/2) = 2*4=8.
The answer should be simplified: as 768=3*2^8, then x=-8+i*128*3^1/2