Solve the following equation for $x$ :
$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$ .

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Solution

Using dhavachrvy formula
$x = \frac{a (a + b) \pm \sqrt{81 (a^{2} + b^{2} + 2 a b) - 36} (2 a^{2} + 5 a b + 2 b^{2})}{18}$
$= \frac{a (a + b) \pm \sqrt{9 a^{2} + a b^{2} - 18 a b}}{18}$
$= \frac{a (a + b) + 3 a - 3 b}{18}; \frac{a (a + b) - 3 a + 3 b}{18}$
$= \frac{2 a - b}{3}; \frac{2 b - a}{3}$ all the same

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