If $-6\leq a \leq -2$ and $3 \leq b \leq 5$, what is the greatest possible value of $\displaystyle\left(a+\frac{1}{b}\right)\left(\frac{1}{b}-a\right) $? Express your answer as a common fraction.

HumenBeing Jul 11, 2023

#1**-1 **

We have that \begin{align*} (a + 1/b)(1/b - a) &= \frac{a^2}{b} - 1 \ &\ge \frac{(-6)^2}{5} - 1 = -\frac{191}{5}. \end{align*}

Equality occurs when a=−6 and b=5, so the maximum possible value is -191/5.

Guest Jul 11, 2023

#4**0 **

Cause most of the time, for every question I ask, people post incorrect answers, which doesn't help at all.

HumenBeing Jul 19, 2023