Question

if
${x}^{a} = {y}^{b} = {z}^{c} and \: xyz = 1 \: find \: the \: value \: of \: \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$
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Answer 1

Answer:

$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$

Step-by-step explanation:

$let \: {x}^{a} = {y}^{b} = {z}^{c} = k \\ x = {k}^{ \frac{1}{a} } \: \: \: \: y = {k}^{ \frac{1}{b} } \: \: \: \: z = {k}^{ \frac{1}{c} } \\ xyz = 1 - - - - - - (given) \\ {k}^{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} = {k}^{1} \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$