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If l,m,n, be the three positive roots of...

If `l,m,n,` be the three positive roots of the equation `x^(3)-ax^(2)+bx-48=0`, then the minimum value of `(1)/(l)+(2)/(m)+(3)/(n)` equals `(alpha)/(beta)` where `alpha,beta in N` , `gcd(alpha,beta)=1` then `alpha^(2)+beta^(2)=`

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