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已知

a>\frac{1}{2}, b>\frac{1}{3} ， \frac{1}{a}+\frac{2}{b}=7

，则 $\frac{3}{2 a-1...

Mar 8, 2024

已知 a>\frac{1}{2}, b>\frac{1}{3} ， \frac{1}{a}+\frac{2}{b}=7 ，则

\frac{3}{2 a-1}+\frac{1}{3 b-1}

的最小值

Generated Graph

Solution by Steps

step 1

Given the constraints a>\frac{1}{2} and b>\frac{1}{3}, we need to solve the equation

\frac{1}{a}+\frac{2}{b}=7

step 2

From the asksia-ll calculation, we have the solution for

a

and

b

as 1/2<a<1 and

b = \frac{2a}{7a - 1}

step 3

To find the minimum value of

\frac{3}{2a-1}+\frac{1}{3b-1}

, we substitute

b

with

\frac{2a}{7a - 1}

in the expression

step 4

The asksia-ll calculator found no global minima for the expression

\frac{3}{2a-1}+\frac{1}{3b-1}

Answer

There is no global minimum for the expression

\frac{3}{2a-1}+\frac{1}{3b-1}

under the given constraints.

Key Concept

Solving a system of inequalities and finding the minimum value of an expression

Explanation

The system of inequalities was solved to express

b

in terms of

a

. However, upon attempting to minimize the given expression, no global minimum was found within the specified domain for

a

and

b