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Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x. - Mathematics

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Questions

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

Solve by completing the square:

x2 – 2ax + (a2 – b2) = 0

Sum
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Solution

We have, x2 – 2ax + (a2 – b2) = 0

⇒ x2 – ((a + b) + (a – b))x + (a2 – b2) = 0

⇒ x2 – (a + b)x – (a – b)x + (a + b) (a – b) = 0   ...[∵ a2 – b2 = (a + b) (a – b)]

⇒ x(x – (a + b)) – (a – b) (x – (a + b)) = 0

⇒ (x – (a + b)) (x – (a – b) = 0

⇒ x = a + b, a – b

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Chapter 5: Quadratic equations - Exercise 5C [Page 70]

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