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Diano4ka-milaya [45]
2 years ago
5

The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pai

rs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.
Mathematics
1 answer:
olasank [31]2 years ago
7 0

Answer:

Conjecture :  2xy / ( x + y ) ≤  √xy

Step-by-step explanation:

Harmonic mean of  x and y = 2xy/( x + y )

<u>Formulate a conjecture about their relative sizes </u>

we will achieve this by computing harmonic and geometric means

Geometric mean = √xy

harmonic mean = 2xy/( x + y )

Conjecture :  2xy / ( x + y ) ≤  √xy

attached below is the proof

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