Question

x root a= y root b =z root c and ABC=1 then prove that x+y+z=0​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \sqrt[x]{a} = \sqrt[y]{b} = \sqrt[z]{c} \: \: and \: \: abc = 1 }$

TO PROVE

x + y + z = 0

EVALUATION

Let

$\displaystyle \sf{ \sqrt[x]{a} = \sqrt[y]{b} = \sqrt[z]{c} = k}$

Then

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

$\displaystyle \sf{ \implies \: a = {k}^{x} \: , \: b = {k}^{y} \: ,\: c = {k}^{z} }$

Now

$\displaystyle \sf{ abc = 1}$

$\displaystyle \sf{ \implies \: {k}^{x} . {k}^{y} . {k}^{z} = 1 }$

$\displaystyle \sf{ \implies \: {k}^{x + y + z} = 1 }$

$\displaystyle \sf{ \implies \: {k}^{x + y + z} = {k}^{0} }$

$\displaystyle \sf{ \implies \: {x + y + z} = {0} }$

Hence proved

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Answer 2

Answer:

Step-by-step explanation: