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If a > 0 and
\( a - \frac{1}{a} = \frac{5}{6},\)
then

\( a + \frac{1}{a} = \ ? \)

 Jun 25, 2020
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\(a-\frac{1}{a}=\frac{5}{6}\)

Multiply a on both sides:

\(a^2-\frac{5}{6}a-1=0\)

Using the quadratic formula, (\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)) you get two roots. One is positive, one is negative. Use the positive one because a > 0.

That root is \(\boxed{\frac{13}{6}}\)

 
 Jun 25, 2020
edited by amazingxin777  Jun 25, 2020
edited by amazingxin777  Jun 25, 2020

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