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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
hope it helps you....
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