Question Number 10005 by konen last updated on 20/Jan/17

(x^(1/(16)) +1)(x^(1/8) +1)(x^(1/4) +1)(x^(1/2) +1)=?

Answered by mrW1 last updated on 21/Jan/17

P=(x^(1/(16)) +1)(x^(1/8) +1)(x^(1/4) +1)(x^(1/2) +1) if x=1: P=(1+1)^4 =2^4 =16 if x≠1: (x^(1/(16)) −1)P=(x^(1/(16)) −1)(x^(1/(16)) +1)(x^(1/8) +1)(x^(1/4) +1)(x^(1/2) +1) (x^(1/(16)) −1)P=(x^(1/8) −1)(x^(1/8) +1)(x^(1/4) +1)(x^(1/2) +1) (x^(1/(16)) −1)P=(x^(1/4) −1)(x^(1/4) +1)(x^(1/2) +1) (x^(1/(16)) −1)P=(x^(1/2) −1)(x^(1/2) +1) (x^(1/(16)) −1)P=(x−1) P=((x−1)/(x^(1/(16)) −1))