+0

# If $-5\leq a \leq -1$ and $1 \leq b \leq 3$, what is the least possible value of

0
63
4
+467

$$\displaystyle\left(\frac{1}{a}+\frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right)$$

Dec 4, 2020

#1
0

To minimize (1/a + 1/b)(1/b - 1/a), we take a = -5 and b = 1.  This gives us a minimum value of 24/25.

Dec 4, 2020
#2
0

The least possible value occurs when:

a = - 1   and   b = 3, which gives the result of:

- 8 / 9 - The least possible value.

Dec 4, 2020
#3
+467
0

Thanks for trying my problems

Dec 7, 2020
#4
+112080
+1

Can you please put the question in the question box.

You can put something similar in the heading as well if you want but ALL the question needs to be in the question box.

Dec 7, 2020