Question

Please tell me. Who will give correct answer I'll make him or her brainliest.​​

Answer 1

EXPLANATION.

x, y, z are positive real numbers.

p, q, r are natural numbers.

$\sf \implies x^{p} = y^{q} = r^{z}$

$\sf \implies \dfrac{y}{x} = \dfrac{z}{y}$

As we know that,

Let us considered as,

$\sf \implies x^{p} = y^{q} = r^{z} = k \ (say).$

$\sf \implies x^{p} = k$

$\sf \implies x = k^{1/p} . - - - - - (1).$

$\sf \implies y^{q} = k$

$\sf \implies y = k^{1/q} . - - - - - (2).$

$\sf \implies z^{r} = k$

$\sf \implies z = k^{1/r} . - - - - - (3).$

$\sf \implies \dfrac{y}{x} = \dfrac{z}{y}$

$\sf \implies y^{2} = zx$

Put the values in the equation, we get.

$\sf \implies (k^{1/q} )^{2} = (k^{1/p} ).(k^{1/r} )$

$\sf \implies (k^{2/q} ) = (k^{1/p + 1/r} )$

$\sf \implies \dfrac{2}{q} = \dfrac{1}{p} + \dfrac{1}{r}$

Hence Proved.

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

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