Descartes' Rule of Signs

Algebra Level 2

The function \(f(x)=x^4+ax^3+bx^2+cx+d\) has four positive roots. We are also given that \((b-a)(a+b)+(d-c)(c+d)=2(ac-bd).\)

What is the value of \((a+b+c+d)^2?\)

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