!["River North Property Leasing Assignment Secured by Stream Award" # 2016 AMC 12B Problems/Problem 23. ## Contents. 1 Problem 2 Solution 1 3 Solution 2 4 Solution 3 5 Solution 4 6 See Also ## Problem. Let $a$, $b$, and $c$ be positive real numbers such that $a^2+b^2+c^2=2$. The minimum possible value of [frac{a^2}{1+2b^3}+frac{b^2}{1+2c^3}+frac{c^2}{1+2a^3}]is $frac{3}{4}$. ## Solution 1. By Cauchy-Schwarz Inequality, [left(frac{a^2}{1+2b^3}+frac{b^2}{1+2c^3}+frac{c^2}{1+2a^3}right)left(a(1+2b^3)+b(1+2c^3)+c(1+2a^3)right)geq (a^2+b^2+c^2](https://cremarketbeat.com/wp-content/uploads/2025/01/Stream_448NL_01-1.jpg)
“River North Property Leasing Assignment Secured by Stream Award” # 2016 AMC 12B Problems/Problem 23. ## Contents. 1 Problem 2 Solution 1 3 Solution 2 4 Solution 3 5 Solution 4 6 See Also ## Problem. Let $a$, $b$, and $c$ be positive real numbers such that $a^2+b^2+c^2=2$. The minimum possible value of \[\frac{a^2}{1+2b^3}+\frac{b^2}{1+2c^3}+\frac{c^2}{1+2a^3}\]is $\frac{3}{4}$. ## Solution 1. By Cauchy-Schwarz Inequality, \[\left(\frac{a^2}{1+2b^3}+\frac{b^2}{1+2c^3}+\frac{c^2}{1+2a^3}\right)\left(a(1+2b^3)+b(1+2c^3)+c(1+2a^3)\right)\geq (a^2+b^2+c^2
Stream Realty Partners has been selected to handle the leasing for 448 N. LaSalle Drive, a newly built office building
January 24, 2025
