Exponents 1

If x^(1/m)=y^(1/n)=z^(1/p) and xyz=1 , find m + n + p

2 Answers

337

Sayan Sinha ·2013-06-23 11:57:00

Let x^{^1m}+y^¹ⁿ+z^{^1p} = k.

So, x=k^m; y=kⁿ; z=k^p

xyz=1
â†’k^mkⁿk^p=1
â†’k^(m+n+p)=1
â†’m+n+p=0 if kâ‰ 1.
If k=1, m+n+p can have any value, including 0.

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Sayantan Hazra even if k = 1, (m + n + p)can be zero........ :)
Upvote·0· Reply ·2013-06-27 05:04:34
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K^m+ⁿ+^p=1¹=1⁰

So, m+n+p=0 or 1,

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Sayan Sinha only when k=1, as I have already mentioned. ..
Upvote·0· Reply ·2013-07-06 10:14:08
Samaroha Nandi It will be correct.
Upvote·0· Reply ·2013-07-08 09:55:11
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