how is it possible that a formula can be true if...........?

Question

I was doing matter in my physics course and i was working on derviving a formula for potential energy of atoms when forced out of equilibrium, but from the initial form of 0= e [ K^16 - 2*K^6 ]
When derviving you get the form K^16 = 2*K^6
(when K is equilibrium seperation over displacement, but their both the same figures, i think )
But yeah, i can see how you get there but that doesn't make sense mathematically and surely isnt true, so how can the final form be true if that isn't?
( r = r' / 2^1/6 )

im just saying
K^16=2*K^6
if you plug in a figure like 2
2^16 is not equal to 2*2^6

Answer 1

Ug

Answer 2

Some questions for you :
Why isnt it correct :?

if this is correct then the rest of your derivation is correct as well

0= e [ K^16 - 2*K^6 ]


K^16 = 2*K^6 => K = 0.5 ^-10

i dont see the problem