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已知

a, b ， c

是正实数, 且

b+c=\sqrt{6}

，则

\frac{a c^{2}+2 a}{b c}+\frac{8}{a+1}

...

Mar 8, 2024

已知

a, b ， c

是正实数, 且

b+c=\sqrt{6}

，则

\frac{a c^{2}+2 a}{b c}+\frac{8}{a+1}

最小值为

Solution by Steps

step 1

Given the function

f(a, b, c) = \frac{a c^{2}+2 a}{b c}+\frac{8}{a+1}

with the constraint

b+c=\sqrt{6}

, we are to find the minimum value for

f

with respect to

a, b,

and

c

step 2

The asksia-ll calculator was used to attempt to find the global minimum of the function under the given domain

step 3

The result from the asksia-ll calculator indicated that no global minima were found for the function with the given constraint

Answer

No global minimum value can be found for the given function under the constraint

b+c=\sqrt{6}

Key Concept

Optimization with constraints

Explanation

In some optimization problems with constraints, a global minimum may not exist, or the methods used may not be able to find one. This is the case with the given function and constraint.