Let \( a, b, c, d \) are distinct real numbers and \( a, b \) are the roots of the quadratic equ...

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Let \( a, b, c, d \) are distinct real numbers and \( a, b \) are the roots of the quadratic equation \( x^{2}-2 c x-5 d=0 \). If \( c \) and \( d \) are the roots of the quadratic equation \( x^{2}-2 a x-5 b=0 \), the sum of the digits of numerical values of \( a+b+c+d \) is
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