If L, m, n be the three positive roots of the equation x3 -ax2 +bx -48 = 0 then the minimum value 1/L + 2/m + 3/n =a) 1b) 2c) 3/2d) 5/2

Dear Ajay

You have to apply Airthmetic mean(AM)≥Geometric mean(GM)

AM=(1/L + 2/m + 3/n)/3

GM=(1/L*2/m*3/m)^1/3=(6/Lmn)^1/3

From cubic equation product of roots Lmn=-(-48/1)=48

GM=(6/48)^1/3 = (1/8)^1/3=1/2

apply AM≥GM

(1/L + 2/m + 3/n)/3 ≥ 1/2

(1/L + 2/m + 3/n) ≥ 3/2

hence min value is 3/2  option c

All the best.                                                           

AKASH GOYAL

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