SOLUTION: hey what will be the solution for following according to you all {{{ x^(1/p)=y^(1/q)=z^(1/r) }}} and x.y.z = 1 then what will be value of p+q+r ?

Algebra ->  Exponents -> SOLUTION: hey what will be the solution for following according to you all {{{ x^(1/p)=y^(1/q)=z^(1/r) }}} and x.y.z = 1 then what will be value of p+q+r ?      Log On


   

Question 190125: hey what will be the solution for following according to you all
+x%5E%281%2Fp%29=y%5E%281%2Fq%29=z%5E%281%2Fr%29+
and x.y.z = 1
then what will be value of p+q+r ?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let
+x%5E%281%2Fp%29=y%5E%281%2Fq%29=z%5E%281%2Fr%29=t+
Then
from +x%5E%281%2Fp%29=t+, we obtain x=t%5Ep
For the same reason, we have
y=t%5Eq
and
z=t%5Er
Substituting them into xyz=1, we have
%28t%5Ep%29%28t%5Eq%29%28t%5Er%29=1, or written as:
t%5E%28p%2Bq%2Br%29=1
The equation implies that:
p%2Bq%2Br=0