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If the sum of the roots of the quadratic equation `ax^(2) + bx + c = 0` is equal to the sum of the squares of their reciprocals, then prove that `2a^(2)c = c^(2)b + B^(2)a.`

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The correct Answer is:
`2a^(2)c = c^(2)b + b^(2)a`
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