Solve the following quadratic equations by factorization method :
$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$

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Solution

$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$
$⟹ 9 x^{2} - 9 (a + b) x + [2 a (a + 2 b) + b (a + 2 b)] = 0$
$⟹ 9 x^{2} - 9 (a + b) x + [(2 a + b) (a + 2 b)] = 0$
$⟹ 9 x^{2} - 3 [(a + 2 b) (2 a + b)] x + [(2 a + b) (a + 2 b)] = 0$
$⟹ 3 x [3 x - (a + 2 b)] [3 x - (2 a + b)] = 0$
$⟹ 3 x = a + 2 b$
$⟹ x = \frac{a + 2 b}{3}$
or,
$⟹ 3 x = 2 a + b$
$⟹ x = \frac{2 a + b}{3}$

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Similar questions

Solve the following quadratic equation using quadratic formula .

$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$

9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0

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9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0

9 x^{2} - 9 (a + b) x + (2 a 62 + 5 a b + 2 b^{2}) = 0

9 x^{2} - 9 (a + b) + (2 a^{2} + 5 a b + 2 b^{2}) = 0

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