Help with solving complex radical equation?

Question

The equation is

(x-2) under a radical) - (47-x) under a radical) = 9

Any suggestions?? It would be greatly appreciated.

Answer 1

I tried to solve it using ln, as in

0.5 ln (x-2) - 0.5 ln (47-x) = ln 9

0.5 ln [(x-2) / (47-x)] = ln 9

ln [(x-2) / (47-x)] = 2 ln 9

removing ln from both sides,

(x-2) / (47-x) = 4.394

which gives me x = 38.65

When I put it back in the equation to check, I do not get the right answer! However, maybe I'm making an error which you can point out? Try this method and see where the mistake lies.

Answer 2

1)x>=2 and x<= 47

sqrt(x-2) = 9+sqrt(47-x) now both sides are positive and you can square

x-2 = 81+47-x+18 sqrt(47-x)

2x-130=18sqrt(47-x)

x-65=9sqrt(47-x)  so x must be >65 which is impossible so there are no solutions.No further work needed