Question

please solve this question.
if you know.
good morning to all .
I am going off now​

Answer 1

Q.No.22

Given,

${x}^{p} = {y}^{q} = {z}^{r}$

To prove;

To prove:

$\frac{2}{q } = \frac{1}{p} + \frac{1}{r}$

We have,

$\frac{y}{x} = \frac{z}{y} \\ \\ {y}^{2} = xz \\ \\ ({ {y}^{q} })^{ \frac{2}{q} } = ({x}^{p}) {}^{ \frac{1}{p} } . ({z}^{r}) {}^{ \frac{1}{r} } \\ \\ ({y}^{q}) {}^{ \frac{2}{q} } = ({y}^{q}) {}^{ \frac{1}{p} } .(y {}^{q}) {}^{ \frac{1}{r} } \\ \\ (y {}^{q}) {}^{ \frac{2}{q} } = (y {}^{q}) {}^{ \frac{1}{p} + \frac{1}{r} } \\ \\ \frac{2}{q } = \frac{1}{p} + \frac{1}{r}$

Proved.