If \( \alpha, \beta, \gamma, \delta \) are the roots of the equation \( x^4 - 10x^3 + 35x^2 - 50x + 24 = 0 \) and \( \alpha^2, \beta^2, \gamma^2, \delta^2 \) are the roots of the equation \( x^4 + ax^3 + bx^2 + cx + d = 0 \), then \( a = \)
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Use the identity \( \sum \alpha_i^2 = (\sum \alpha_i)^2 - 2\sum \alpha_i\alpha_j \). Here, \( a = -(10^2 - 2(35)) = -(100 - 70) = -30 \). This works even if the roots aren't easy to find.