Question

if b is mean proportional between and c then (a^2-b^2+c^2)/(a^-2-b^-2+c^-2)=?

Answer 1

Hi ,

If b is the mean Proportion of a and

b then

b² = ac ---( 1 )

Now ,

( a² + b² + c² )/( a^-2 + b^-2 + c^-2 )

= ( a² + b² + c² )/( 1/a² + 1/b² + 1/c² )

= (a² + ac + c² )/( 1/a² + 1/ac + 1/c² )

[ From ( 1 ) ]

= (a² + ac + c²)/[(c²+ ac + a²)/a²c²

= [ a²c² (a²+ ac+ c²)/( a² + ac + c² )]

= a²c²

I hope this helps you.

: )

Answer 2

Answer:

Hi ,

If b is the mean Proportion of a and

b then

b² = ac ---( 1 )

Now ,

( a² + b² + c² )/( a^-2 + b^-2 + c^-2 )

= ( a² + b² + c² )/( 1/a² + 1/b² + 1/c² )

= (a² + ac + c² )/( 1/a² + 1/ac + 1/c² )

[ From ( 1 ) ]

= (a² + ac + c²)/[(c²+ ac + a²)/a²c²

= [ a²c² (a²+ ac+ c²)/( a² + ac + c² )]

= a²c²

I hope this helps you.