Prove that if $abc \geq 1$ and $a,b,c > 0$ then, $$\frac{1}{1 + a + b} + \frac{1}{1 + b + c} + \frac{1}{1 + c + a} \leq 1$$
Can anyone help me with this problem?
Tried AM-GM and Cauchy-Schwarz inequality, but it didn't work.
2026-03-25 09:43:09.1774431789
Prove that if $abc \geq 1$ and $a,b,c > 0$ then $\frac{1}{1 + a + b} + \frac{1}{1 + b + c} + \frac{1}{1 + c + a} \leq 1$
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