If a^p=b^q=c^r=abc then find pqr=?
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Answered by
100
Hello dear,
Given that a^p=abc so a=(abc)^1/p
Similarly
b=(abc)^1/q and
c=(abc)^1/r
Now 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
Given that a^p=abc so a=(abc)^1/p
Similarly
b=(abc)^1/q and
c=(abc)^1/r
Now 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
rohitkumargupta:
thanks dear
it ok
hn
Answered by
2
Answer: pq+qr+rs
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