#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 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

419 Points
11 years ago

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

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.