Question

Calculate a+b+c if x to the power 1/a=y to the power 1/b=z to the power1/c and xyz =1

Answer 1

replace value of y and. z by x

Answer 2

Hi...☺

Here is your answer...✌

GIVEN THAT,

${x}^{ \frac{1}{a} } = {y}^{ \frac{1}{b} } = {z}^{ \frac{1}{c} }$

LET,

${x}^{ \frac{1}{a} } = {y}^{ \frac{1}{b} } = {z}^{ \frac{1}{c} } = p$

We have ,

${x}^{ \frac{1}{a} } =p \\ \\ x = {p}^{a}$

Similarly,

$y = {p}^{b} \: \: and \: \: z = {p}^{c}$

Also given that

$xyz = 1 \\ \\ {p}^{a} \times {p}^{b} \times {p}^{c} = {p}^{0} \: \: \: \: \: \: \: \: \: \: \: \: \: | \because {p}^{0} = 1 | \\ \\ {p}^{a + b + c} = {p}^{0} \\ \\ on \: \: equating \: \: power \: \: of \: \: p \\ we \: \: get \\ \\ a + b + c = 0$