Unique Quadrata

Algebra Level 4

\(a, b, c, d \) are distinct numbers such that:

  • \(a\) and \(b\) are the roots of the equation \(x^2-2cx-5d=0\)
  • \(c\) and \(d\) are the roots of the equation \(x^2-2ax-5b=0\)

Find the value of \(a+b+c+ d \).

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