Question

if a^1/m=b^1/n=c^1/p and abc=1 then find the value of m+n+p​

Answer 1

$m+n+p=0$

Step-by-step explanation:

Let, $a^{1/m}=b^{1/n}=c^{1/p}=k$, where $k\neq 0$

Then,

• $a^{1/m}=k\Rightarrow a=k^{m}$

• $b^{1/n}=k\Rightarrow b=k^{n}$

• $c^{1/p}=k\Rightarrow c=k^{p}$

Given, $abc=1$

$\Rightarrow k^{m}\times k^{n}\times k^{p}=1$

$\Rightarrow k^{m+n+p}=k^{0}$

• Using $a^{m}\times a^{n}\times a^{p}=a^{m+n+p}$

• and $a^{0}=1$

Now, comparing both sides, we get

$m+n+p=0$

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