Solve $a b x^{2} - (a^{2} + b^{2}) x + a b = 0$

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Solution

Consider the given equation.
$a b x^{2} - (a^{2} + b^{2}) x + a b = 0$
$a b x^{2} - a^{2} x - b^{2} x + a b = 0$
$a x (b x - a) - b (b x - a) = 0$
$(a x - b) (b x - a) = 0$
$a x - b = 0$ or $b x - a = 0$
$a x = b$ or $b x = a$
$x = \frac{b}{a}$ or $x = \frac{a}{b}$

Hence, this is the answer.

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