0

Guest

Courses New

if a+b+c=6 and a,b,c E R + then prove that 1/a+4/b+9/c＞=6

if a+b+c=6 and a,b,c E R+ then prove that 1/a+4/b+9/c＞=6

Grade:12th pass

1 Answers

Aditi singh
15 Points
5 years ago
a+b+c=6 can also be written as a+b/2+b/2+c/3+c/3+c/3=6  so, according to the formula of AM≥HM which is a+b+c÷3≥3÷1/a+1/b+1/c.       
So, here 
a+b/2+b/2+c/3+c/3+c/3÷6≥6÷1/a+4/b+9/c 
6÷6≥6÷1/a+4/b+9/c (according to data)
1≥6÷1/a+4/b+9/c
So,1/a+4/b+9/c≥6 
Hence proved
1

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More