If \( b \) is a mean proportional between \( a \) and \( c \), prove that \[ \frac{-a^{2}-b^{2}+...

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If \( b \) is a mean proportional between \( a \) and \( c \), prove that
\[
\frac{-a^{2}-b^{2}+c^{2}}{a^{-2}-b^{-2}+c^{-2}}=b^{4} \text {. }
\]
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