Question

If y is the mean proportional between x and z
prove that ;
$( {x}^{2} - {y }^{2} + {z}^{2}) \div ( {x}^{ - 2} - {y}^{ - 2} + {z}^{ - 2} ) = {y}^{4}$
this is equation to prove​

Answer 1

Answer:

We have,

y is the mean proportional between x+z then,

y  

2

=xz

⇒y=  

xy

​  

 

​  

 

To prove xyz(x+y+z)  

3

=(xy+yz+zx)  

3

 

R.H.S

(xy+yz+zx)  

3

 

=(xy+yz+zx)  

3

 

=y  

3

(x+y+z)  

3

 

=y  

2

.y(x+y+z)  

3

 

=zx.y(x+y+z)  

3

 

=xyz(x+y=z)  

3

 

​  

 

L.H.S

Hence, proved.

Explanation: