Show that \( a^{2}, b^{2}, c^{2} \) are in A.P. iff \( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+...

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Show that \( a^{2}, b^{2}, c^{2} \) are in A.P. iff \( \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b} \) are in A.P.
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