If $a$ and $b$ are positive real numbers with sum $3$, and $x, y, z$ positive real numbers with product $1$, prove that : $(ax+b)(ay+b)(az+b)\geq 27$
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Tags: inequalities, algebra
If $a$ and $b$ are positive real numbers with sum $3$, and $x, y, z$ positive real numbers with product $1$, prove that : $(ax+b)(ay+b)(az+b)\geq 27$