A strange equation VI

Algebra Level 3

If one root of the equation x44x316x28x+4=0x^4-4x^3-16x^2-8x+4=0 can be expressed as a+b+c+da+\sqrt{b}+\sqrt{c}+\sqrt{d} where bb, cc and dd are square-free numbers, then find a+bcda+bcd.

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