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```        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) 1
b) 2
c) 3/2
d) 5/2

```
6 years ago

419 Points
```										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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```
6 years ago
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