Find the roots of the following quadratic equations,if they exist,using the quadratic formula of shridhar Acharya.
$x + \frac{1}{x} = 3, x \neq 0$

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Solution

rearranging
$x^{2} - 3 x + 1 = 0$
by shridhar acharya's formula to test existence of the roots, we have
$b^{2} - 4 a c = (3)^{2} - 4 * 1 * 1 = 5$
$∴$ root exists and they are distinct

$x 1 = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ and $x 2 = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$

$x 1 = \frac{- 3 + \sqrt{5}}{2 * 1} = - 0.382$ and $x 2 = \frac{- 3 - \sqrt{5}}{2 * 1} = - 2.618$

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