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anemone
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Let $a,\,b$ and $c$ be positive real numbers. Determine the minimum value of $\dfrac{a+3c}{a+2b+c}+\dfrac{4b}{a+b+2c}+\dfrac{8c}{a+b+3c}$.
The formula for the expression is Min Value = $\dfrac{a+3c}{a+2b+c}$+$\dfrac{4b}{a+b+2c}$+$\dfrac{8c}{a+b+3c}$.
The variable a represents the first number in the expression, b represents the second number, and c represents the third number.
Finding the minimum value of this expression can help in solving optimization problems, where the goal is to find the smallest possible value that satisfies certain constraints.
No, this expression cannot have a negative minimum value because all the terms in the expression are positive.
Yes, the minimum value of this expression can be found by using the AM-GM inequality, which states that the arithmetic mean of a set of positive numbers is greater than or equal to the geometric mean of the same set of numbers. By applying this inequality to the expression, we can find the minimum value.