The ratio of the A.M and G.M. of two positive numbers a and b, is m: n. Show that .

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Solution

Let the two numbers be a and b.

A.M and G.M. =

According to the given condition,

Using this in the identity (a – b)² = (a + b)² – 4ab, we obtain

Adding (1) and (2), we obtain

Substituting the value of a in (1), we obtain

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The ratio of the A.M and G.M. of two positive numbers a and b, is m: n. Show that .

Let the two numbers be a and b. A.M and G.M. = According to the given condition, Using this in the identity (a – b)2 = (a + b)2 – 4ab, we obtain Adding (1) and (2), we obtain Substituting the value of a in (1), we obtain

Let the two numbers be a and b.

A.M and G.M. =

According to the given condition,

Using this in the identity (a – b)² = (a + b)² – 4ab, we obtain

Adding (1) and (2), we obtain

Substituting the value of a in (1), we obtain