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(C) Let $a^2(a + p) = b^2(b + p) = c^2(c + p) = k$.This implies that $a, b, c$ are the roots of the cubic equation $x^2(x + p) = k$,which can be rewri

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(C) Let $a^2(a + p) = b^2(b + p) = c^2(c + p) = k$.This implies that $a, b, c$ are the roots of the cubic equation $x^2(x + p) = k$,which can be rewritten as $x^3 + px^2 - k = 0$.For a cubic equation of the form $Ax^3 + Bx^2 + Cx + D = 0$,the sum of the product of roots taken two at a time is given by $\frac{C}{A}$.In the equation $x^3 + px^2 + 0x - k = 0$,we have $A = 1, B = p, C = 0, D = -k$.Therefore,$bc + ca + ab = \frac{C}{A} = \frac{0}{1} = 0$.

If $3$ distinct real numbers $a, b, c$ satisfy $a^2(a + p) = b^2(b + p) = c^2(c + p)$ where $p \in R$,then the value of $bc + ca + ab$ is

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