Happy 25 followers!

Algebra Level 5

x 2 y + z + y 2 x + z + z 2 x + y \dfrac{x^{2}}{y+z}+\dfrac{y^{2}}{x+z}+\dfrac{z^{2}}{x+y} Given that, x + y + z = n x+y+z=n . If x , y , z x,y,z are positive real numbers, and the minimum value of the expression above can be expressed as 25 p n 25pn . What is the value of p p ?

Give your answer up to 2 decimal places


The answer is 0.02.

I Gede Arya Raditya Parameswara by I Gede Arya Raditya Para… , 17

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Spandan Senapati
May 24, 2017

Use Titus Lemma a 2 / x + b 2 / y + c 2 / z > = ( a + b + c ) 2 / ( x + y + z ) a^2/x+b^2/y+c^2 /z>=(a+b+c)^2/(x+y+z) . This yields the minimum value as x + y + z / 2 = n / 2 x+y+z/2=n/2 so p = 1 / 50 = 0.02 p=1/50=0.02

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...