Solve the following quadratic equation

Q) Solve the following quadratic equation by factorization method.

$\frac{1}{\times - 2} + \frac {2}{\times - 1} = \frac{6}{\times}$

Ans:

Let’s find out the hidden quadratic equation:

$\frac{1}{\times - 2}+\frac{2}{\times - 1} = \frac{6}{\times}$

∴ $\frac{(\times - 1) + 2(\times - 2)}{(\times-2)(\times-1)} = \frac{6}{\times}$

∴ $\frac{3\times - 5}{\times^{2} - 3\times + 2} = \frac{6}{\times}$

∴ X (3 X – 5) = 6 (X² – 3 X + 2)

∴ 3 X²– 5X = 6X²– 18X + 12

∴ 3X²-13 X + 12 = 0

∴ 3 X² – 9X – 4X + 12 = 0

∴ 3 X(X – 3) – 4 (X – 3) = 0

∴ (X – 3) (3 X – 4) = 0

∴ therefore the roots are X = 3 and X = $\frac{4}{3}$

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