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Solve the following quadratic equation for x: x^2 – 2ax – (4b^2 – a^2) = 0 - Mathematics

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Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0

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Solution

x2 – 2ax – (4b2 – a2) = 0
⇒ x2 + (2b – a)x – (2b + a)x – (4b2 – a2) = 0
⇒ x(x + 2b – a) – (2b + a)(x + 2b – a) = 0
⇒ (x + 2b – a)(x – 2b – a) = 0
⇒ (x + 2b – a) = 0, (x – 2b – a) = 0
∴ x = a − 2b, a + 2b

Concept: Solutions of Quadratic Equations by Factorization
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