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If λ and M be real numbers such that X 3 -λX 2 +mX-6=0 has its roots real and positive, then minimum value of M is
X3-λX2+mX-6=0 a+b + c = λ ab + bc + ca = m abc = 6 applying A.M. G.M. inequality, (ab + bc + ca )/3 >= ( ab.bc.ca) ^1/3 > = ( abc) ^2/3 > = 6^2/3 (ab + bc + ca ) >= 3 * (6) ^2/3 so its minimum value will be = 3 * (6) ^2/3
X3-λX2+mX-6=0
a+b + c = λ
ab + bc + ca = m
abc = 6
applying A.M. G.M. inequality,
(ab + bc + ca )/3 >= ( ab.bc.ca) ^1/3
> = ( abc) ^2/3
> = 6^2/3
(ab + bc + ca ) >= 3 * (6) ^2/3
so its minimum value will be = 3 * (6) ^2/3
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