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a^p=b^q=C^r=abc then pqr=?

a^p=b^q=C^r=abc then pqr=?

Grade:9

3 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
8 years ago
We have:
a^p=b^q=c^r=abc\Rightarrow a^pb^qc^r=(abc)(abc)(abc)=a^3 b^3 c^3.
Hence,
pqr=3\times3\times3=27
sumit kumar pathak
20 Points
7 years ago
a^p=abc so a=(abc)^1/psimilarly b=(abc)^1/qand c=(abc)^1/rtherefore abc = (abc)^1/p+1/q+1/r=> 1=(p+q+r)/(pqr)=> pqr = p+q+r
Ramesh
11 Points
6 years ago
Given that a^p=abc so a=(abc)^1/pSimilarly b=(abc)^1/q and c=(abc)^1/rNow abc=(abc)^1/p.(abc)^1/q.(abc)^1/r=>abc=(abc)^1/p+1/q+1/r=>1=1/p+1/q+1/r=>1=(qr+pr+pq)/pqr=>pqr=pq+qr+rp

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