Question

(x-2)^(2/3)+(x-2)^(1/3)-12=0

Answer 1

let u=(x-2)^(1/3)
then u^2=(x-2)^(2/3)

so we have u^2+u-12=0
(u+4)(u-3)=0
u=-4, u=3
but remember u=(x-2)^(1/3)
so
solve (x-2)^(1/3)=-4 and (x-2)^(1/3)=3 for x