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Mathematics

Solve :

(a + b)2x2 - (a + b)x - 6 = 0; a + b ≠ 0.

Quadratic Equations

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Answer

Let (a + b)x = y

⇒ (a + b)2x2 - (a + b)x - 6 = 0

⇒ y2 - y - 6 = 0

⇒ y2 - 3y + 2y - 6 = 0

⇒ y(y - 3) + 2(y - 3) = 0

⇒ (y + 2)(y - 3) = 0

⇒ (y + 2) = 0 or y - 3 = 0

⇒ y = -2 or y = 3.

∴ (a + b)x = -2 or (a + b)x = 3

⇒ x = −2a+b or 3a+b-\dfrac{2}{a + b} \text{ or } \dfrac{3}{a + b}.

Hence, x = −2a+b or 3a+b.-\dfrac{2}{a + b} \text{ or } \dfrac{3}{a + b}.

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