Y by Adventure10, Mango247
Let
be nonzero real numbers satisfying
. Prove that
![\[\frac{x_1x_2+y_1y_2}{\sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)}}+\frac{x_2x_3+y_2y_3}{\sqrt{(x_2^2+y_2^2)(x_3^2+y_3^2)}}+\frac{x_3x_1+y_3y_1}{\sqrt{(x_3^2+y_3^2)(x_1^2+y_1^2)}} \ge -\frac32.\]](//latex.artofproblemsolving.com/d/9/5/d950afb5656d35bafe5d33cad7addf4c81083021.png)
Ray Li, Max Schindler.


![\[\frac{x_1x_2+y_1y_2}{\sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)}}+\frac{x_2x_3+y_2y_3}{\sqrt{(x_2^2+y_2^2)(x_3^2+y_3^2)}}+\frac{x_3x_1+y_3y_1}{\sqrt{(x_3^2+y_3^2)(x_1^2+y_1^2)}} \ge -\frac32.\]](http://latex.artofproblemsolving.com/d/9/5/d950afb5656d35bafe5d33cad7addf4c81083021.png)
Ray Li, Max Schindler.
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