An algebra problem by Mark Ronel Ocbian

Algebra Level pending

If the arithmetic mean of a two numbers is 10 and the harmonic mean is 360. Find the geometric mean of the numbers.

50 45 55 60

Mark Ronel Ocbian by Mark Ronel Ocbian , 29, Philippines

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1 solution

Syed Baqir
Sep 5, 2015

( A r i t h m e t i c M e a n ) ∗ ( H a r m o n i c M e a n ) = ( G e o m e t r i c M e a n ) 2 ( 10 ) ∗ ( 360 ) = ( G M ) 2 ⇛ G M = 60 (Arithmetic\quad Mean)\quad *\quad (Harmonic\quad Mean)\quad =\quad { (Geometric\quad Mean) }^{ 2 }\\ (10)\quad *\quad (360)\quad =\quad (GM)^{ 2 }\Rrightarrow \quad GM\quad =\quad 60

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