Solve the following equation x14 x12 The solutions of the gi

Solve the following equation. x-1-4 x-1=2 The solution(s) of the given equation is/are x =. (Use a comma to separate answers as needed.)

given

sqrt(x-1) - (x-1)^1/4 =2

let us say sqrt(x-1) =u

so our equation becomes

u - sqrt(u) =2

u-2 = sqrt(u)

squaring on both sides

(u-2)^2 = [sqrtu]^2

u^2 -4u +4 = u

u^2 -4u-u +4=0

u(u-4) -1(u-4) =0

(u-4) (u-1) =0

so u-4 = 0 and (u-1) =0

so u =4 or u=1

but

u =sqrt(x-1)

sqrt(x-1) =1

x-1 =1

x=2

and

sqrt(x-1) = 4

x-1 =16

x =17