Math, asked by Snehaachary3110, 2 months ago

if x y z are in h p then the value of (xz+xy-yz)(xy+yz-xz) /(xyz)²​

Answers

Answered by pulakmath007
2

SOLUTION

GIVEN

x, y , z are in HP

TO DETERMINE

The value of

 \displaystyle \sf{ \frac{(xz + xy - yz)(xy + yz - xz)}{ {(xyz)}^{2} } }

EVALUATION

Here it is given that x, y , z are in HP

 \displaystyle \sf{ \frac{2}{y} =  \frac{1}{x}  +  \frac{1}{z}   }

 \displaystyle \sf{ \implies  \: 2xz = yz + xy}

Now

 \displaystyle \sf{ \frac{(xz + xy - yz)(xy + yz - xz)}{ {(xyz)}^{2} } }

 \displaystyle \sf{ =  \frac{(xz + xy  + xy- 2xz)(2xz - xz)}{ {(xyz)}^{2} } }

 \displaystyle \sf{ =  \frac{(2 xy- xz).xz}{ {(xyz)}^{2} } }

 \displaystyle \sf{ =  \frac{(2y- z). {x}^{2}z }{  {x}^{2} {y}^{2} {z}^{2}   } }

 \displaystyle \sf{ =  \frac{(2y- z) }{  {y}^{2} z   } }

 \displaystyle \sf{ =  \frac{2}{yz}   -  \frac{1}{ {y}^{2} } }

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