Question

Find all possible values of each expression. Suppose 3

Answer 1

The inequality that describes the possible values of the expression is:

$0 < \frac{b}{3a} - \frac{a}{3b} < \frac{9}{60}$

What is the lower bound of values of the expression?

The expression is given by:

$\frac{b}{3a} - \frac{a}{3b}$

To find the lower bound, we try to see when the expression is negative, hence:

$\frac{b}{3a} - \frac{a}{3b} < 0$

$\frac{b}{3a} < \frac{a}{3b}$

Applying cross multiplication and simplifying the 3's, we have that:

$b^2 < a^2$

From the bounds given, this expression will never be true, at most they can be equal, when:

a = b = 4.

Hence the lower bound of values of the expression is of 0.

What is the upper bound of values of the expression?

The expression is a subtraction, hence we want to maximize the first term and minimize the second.

Considering that the first term is direct proportional to b and inverse to a, and the second vice versa, we want to:

• Maximize b, hence b = 5.

• Minimize a, hence a = 4.

Then:

$\frac{b}{3a} - \frac{a}{3b} = \frac{5}{12} - \frac{4}{15} = \frac{25 - 16}{60} = \frac{9}{60}$

Hence the bounds are:

$0 < \frac{b}{3a} - \frac{a}{3b} < \frac{9}{60}$

More can be learned about values of expressions at brainly.com/question/625174

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