SOLUTION: if y is the mean proportional between x and z ; show that xy + yz is the mean proportional between x� + y� and y� + z�

Question 1121372: if y is the mean proportional between x and z ; show that xy + yz is the mean proportional between x� + y� and y� + z�
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
if y is the mean proportional between x and z ;
We know:
= ;
:
show that xy + yz is the mean proportional between x� + y� and y� + z�
=
The easiest to show this is to give some values to x & z
x=2; z=18; then y = = 6
:
=
=
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
We are given that

or

(1)

Then we are to show that

(2)

The algebra for the general case is not terribly difficult....

Equation (2) is equivalent to

Then using equation (1) where appropriate....

Done...!
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