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Let \( a, b, c > 0 \), show that
\[ \sqrt{\frac{11a}{5a+6b}}+\sqrt{\frac{11b}{5b+6c}}+\sqrt{\frac{11c}{5c+6a}} \leq 3. \]
from http://math.stackexchange.com/questions/193568/inequalitysqrtfrac11a5a6bsqrtfrac11b5b6csqrtfrac11c
 one year ago
 one year ago
Let \( a, b, c > 0 \), show that \[ \sqrt{\frac{11a}{5a+6b}}+\sqrt{\frac{11b}{5b+6c}}+\sqrt{\frac{11c}{5c+6a}} \leq 3. \] from http://math.stackexchange.com/questions/193568/inequalitysqrtfrac11a5a6bsqrtfrac11b5b6csqrtfrac11c
 one year ago
 one year ago

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TuringTestBest ResponseYou've already chosen the best response.1
yeah this is gonna be a pain with LaTeX down :S
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
isn't latex working for you? this Q seems fairly complicated ... I've been stalking for more than 2 hrs.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
no, GoDaddy isn't supporting mathjax right now, there is an announcement in the yellow bar on the home page, Why, is it working for you o.O ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
I'm using chrome ... what server does MathJax uses to parse latex?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
not sure, not that tech savvy... but I have chrome as well. do you see the TeX normally or not?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
I see it normally ...
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Let us suppose a is the largest number out of the the three...... then dw:1347343904345:dw will have the largest value.... So now, this value is maximum when a approaches infinity So,dw:1347343979969:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
If a approaches infinity then surely dw:1347344106656:dw will be zero
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
And the term dw:1347344150915:dw also cannot be greater than 1.48
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
as a, or b, or c approaches infinity
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
It will be undefined
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
The maximum value is when a=b=c
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
let a>=b>=c.. now 11a / 5a + 6b = 11/ 5 + 6(b/a) > whole term always less than or equal toone since b>=a thus sqrt (of this) <= 1 for 11b/5b + 6c = 11/5 + 6(c/b) > same thing 11c/5c + 6a = 11(c/a) /5(c/a) + 6 let c/a = m => 11m / 5m + 6 = 11/5 ( m / m + 6/5) = 2.2 ( m + 6/5  6/5) /(m+6/5) =2.2 ( 1  1.2/(m+1.2) ) note that m>=1 for m tends to infinity , max value becomes 2.2 and sqrt(2.2) is approx 1.4 something.. other 2 terms were less than 1 and this one's maxima is 1.4 something,, hence there sum is always less than 3..and equality holds as a=b=c..
 one year ago
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