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IF a+b+c=6. and a,b,c are positive resl no .Prove that1/a+4/b+9/cis greater than equal to6.

Apoorva , 8 Years ago
Grade 11
anser 3 Answers
Ajay

Last Activity: 8 Years ago

From my calculations the smallest value of expression is coming to be 7.
Could you give example values for a,b and c so that expression is 6.

mycroft holmes

Last Activity: 8 Years ago

By Cauchy Schwarz Inequality
 
(a+b+c) \left(\frac{1}{a} +\frac{4}{b} + \frac{9}{c} \right ) \ge (1+2+3)^2 = 36
with equality occurring when a^2=1,b^2=4,c^2=9 i.e. a=1,b=2,c=3.
 
Since a+b+c=6,
 
Hence \frac{1}{a} +\frac{4}{b} + \frac{9}{c} \ge 6
 
Hope this helps

jagdish singh singh

Last Activity: 8 Years ago

Nice Solution hsbhatt Sir

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