<s>[INST] Inequality....(RMO $1994$...question $8$) If $a$, $b$, $c$ are positive real numbers such that $a+b+c = 1$, prove that
$$(1+a)(1+b)(1+c) ≥ 8(1-a)(1-b)(1-c)\text{.}$$
 [/INST] $a+b, c+a$ is positive real,
consider $\frac{1+a}{2}= \frac{(a+b)+(c+a)}{2} \geq \sqrt{(a+b)(c+a)}$
i.e$(1+a)\geq2\cdot\sqrt{(1-c)(1-b)}$
 and so..
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