Math, asked by adityaayushi2712, 2 months ago


 \frac{x + y + z}{ {x}^{ - 1} {y}^{ - 1}  +  {y}^{ - 1}  {z}^{ - 1}  +  {z}^{ - 1}  {x}^{ - 1}  }  = xyz
prove the following

Answers

Answered by Anonymous
2

Step-by-step explanation:

 \huge \underline{ \orange{To  \: Prove:}}

 \bold  \red{ \frac{ x + y + z }{  \blue{ {x}^{ - 1  } {y}^{ - 1}  + {y}^{ - 1}  {z}^{ - 1}  +  {z}^{ - 1}  {x}^{ - 1}  } } } =  \green{xyz}

 \huge \underline{ \gray{ Proof:}}

 \bold\pink{L.H.S.:}

 \bold \red{ \frac{x + y + z}{ \blue{ {x}^{ - 1}  {y}^{ - 1}  +  {y}^{ - 1}  {z}^{ - 1}  +  {z}^{ - 1}  {x}^{ - 1} }} } \\  =   \frac{ \bold \red{x + y + z}}{ \bold \blue{ \frac{1}{xy}  +  \frac{1}{yz}  +  \frac{1}{zx} }}  \\  =  \frac{ \bold \red{x + y + z}}{ \bold \blue{ \frac{z + x + y}{xyz} }}  \\  =  \frac{ \bold \red{(x + y + z)\blue{(xyz)}}}{ \bold \blue{(x + y + z)}}  \\  =  \bold \green {xyz}

 \bold \pink{R.H.S.:}

 \bold \green{xyz}

  \:  \:  \  \:  \:  \:  \:  \:  \: \bold \pink{ { \huge∴} \:  \: L.H.S.= R.H.S.}

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \tt \green{ \underline { \orange{hence \:  \:  proved.}}}

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