Let $ a,b,c$ be real numbers. Prove that $ (ab+bc+ca-1)^2 \le (a^2+1)(b^2+1)(c^2+1)$.
Problem
Source: Indonesia IMO 2007 TST, Stage 2, Test 4, Problem 1
Tags: inequalities, inequalities proposed
Source: Indonesia IMO 2007 TST, Stage 2, Test 4, Problem 1
Tags: inequalities, inequalities proposed
Let $ a,b,c$ be real numbers. Prove that $ (ab+bc+ca-1)^2 \le (a^2+1)(b^2+1)(c^2+1)$.