If \( \mathrm{A} \) is the A.M. between \( a \) and \( b \), prove that \[ (\mathrm{A}-a)^{2}+(\...

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If \( \mathrm{A} \) is the A.M. between \( a \) and \( b \), prove that
\[
(\mathrm{A}-a)^{2}+(\mathrm{A}-b)^{2}=\frac{1}{2}(a-b)^{2}
\]
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