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

 Dec 8, 2020

Best Answer 

 #1
avatar+127 
+1

According to this, your answer would be a,b = -1,3

ay = [-5,-4,-3,-2,-1]
be = [1,2,3]
lo = float('inf')
answr = 0
for a in ay:
    for b in be:
        if (1/a+1/b)*(1/b-1/a) < lo:
            lo = (1/a+1/b)*(1/b-1/a)
            answr = [a,b]
print (lo)
print (answr)

 Dec 8, 2020
 #1
avatar+127 
+1
Best Answer

According to this, your answer would be a,b = -1,3

ay = [-5,-4,-3,-2,-1]
be = [1,2,3]
lo = float('inf')
answr = 0
for a in ay:
    for b in be:
        if (1/a+1/b)*(1/b-1/a) < lo:
            lo = (1/a+1/b)*(1/b-1/a)
            answr = [a,b]
print (lo)
print (answr)

BWStar Dec 8, 2020

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