!["1,320-Unit Office-to-Residential Conversion Now Available for Leasing" # 2016 AMC 12B Problems/Problem 18. ## Contents. 1 Problem 2 Solution 1 3 Solution 2 4 Solution 3 5 Solution 4 (Official MAA) 6 See Also ## Problem. Let $a$, $b$, and $c$ be positive real numbers such that $a^2+b^2+c^2=2$. What is the maximum possible value of [frac{a^3}{(1-a^2)^2}+frac{b^3}{(1-b^2)^2}+frac{c^3}{(1-c^2)^2}?] $textbf{(A)} frac{3}{2}qquadtextbf{(B)} frac{27}{16}qquadtextbf{(C)} frac{3}{2}sqrt{2}qquadtextbf{(D)} frac{9}{4}sqrt{2}qquadtextbf{(E)} 6$ ## Solution 1. By Cauchy-Schwarz Inequality](https://cremarketbeat.com/wp-content/uploads/2025/01/NY-SoMA-exterior-entrance-25-Water-Street-Manhattan.jpg)
“1,320-Unit Office-to-Residential Conversion Now Available for Leasing” # 2016 AMC 12B Problems/Problem 18. ## Contents. 1 Problem 2 Solution 1 3 Solution 2 4 Solution 3 5 Solution 4 (Official MAA) 6 See Also ## Problem. Let $a$, $b$, and $c$ be positive real numbers such that $a^2+b^2+c^2=2$. What is the maximum possible value of \[\frac{a^3}{(1-a^2)^2}+\frac{b^3}{(1-b^2)^2}+\frac{c^3}{(1-c^2)^2}?\] $\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{27}{16}\qquad\textbf{(C)}\ \frac{3}{2}\sqrt{2}\qquad\textbf{(D)}\ \frac{9}{4}\sqrt{2}\qquad\textbf{(E)}\ 6$ ## Solution 1. By Cauchy-Schwarz Inequality
GFP Real Estate, Metro Loft and Rockwood Capital have announced the launch of leasing for SoMA, a luxurious rental tower
Steve Griffin
January 29, 2025
