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G is the geometric mean and p and q are ...

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that :
`G^(2)=(2p-q)(2q-p)`

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AI Generated Solution

To prove that \( G^2 = (2p - q)(2q - p) \) where \( G \) is the geometric mean and \( p \) and \( q \) are the two arithmetic means between two numbers \( a \) and \( b \), we will follow these steps: ### Step 1: Define the geometric mean The geometric mean \( G \) of two numbers \( a \) and \( b \) is given by: \[ G = \sqrt{ab} \] Thus, we have: ...
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