Guest

For positive numbers a,b,c prove that bc/a +ac/b + ab/c is greater than equal to a+b+c

For positive numbers a,b,c prove that bc/a +ac/b + ab/c is greater than equal to a+b+c

 

Grade:9

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

We know that
AM≥GM
(bc/a +ac/b)/2 ​≥ (abc2​/ab)1/2​
⇒(bc/a +ac/b)≥2c...(i)
Similarly
(ac/b +ab/c)​ ≥ 2a...(ii)
(ba/c +bc/a)≥ 2b...(iii)
Now add (i), (ii) & (iii)
bc/a +ac/b + ab/c≥a+b+c

Hence,proved




Thanks

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free