Question Number 10381 by ridwan balatif last updated on 06/Feb/17

Commented byridwan balatif last updated on 06/Feb/17

is there any simple solution to solve this question?

Answered by mrW1 last updated on 06/Feb/17

let t=x^(1/6)   ⇒x=t^6   x^(1/3) =t^2   x^(1/2) =t^3   x^(2/3) =t^4   x^(4/3) =t^8     (((x^(1/3) −x^(1/6) )(x^(1/2) +x)(x^(1/2) +x^(1/3) +x^(2/3) ))/((x^(4/3) −x)(x+x^(1/3) +x^(2/3) )))  =(((t^2 −t)(t^3 +t^6 )(t^3 +t^2 +t^4 ))/((t^8 −t^6 )(t^6 +t^2 +t^4 )))  =(((t−1)(1+t^3 )(t+1+t^2 )t^6 )/((t^2 −1)(t^4 +1+t^2 )t^8 ))  =(((t^3 +1)(t^2 +t+1))/((t+1)(t^4 +t^2 +1)t^2 ))  =(((t+1)(t^2 −t+1)(t^2 +t+1))/((t+1)(t^4 +t^2 +1)t^2 ))  =((t^4 +t^2 +1)/((t^4 +t^2 +1)t^2 ))  =(1/t^2 )=(1/x^(1/3) )=x^(−(1/3))     ⇒ answer (A)