If A,G and H are A.M. , G.M. and H.M. respectively of two positive numbers x and y then prove that G²=AH
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Step-by-step explanation:
A.M. = x + y / 2, G.M. = √xy and H.M. = 2xy / x +y.
L.H.S. = G² = ( √xy )² = xy.
R.H.S. = A. H = [x + y / 2 ] × [ 2xy / x + y ]
= 2xy ( x + y ) / 2 ( x + y )
= xy
∴ L.H.S. = R.H.S.
Hence, It is proved.
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