Solve for x: 4x² – 4ax + (a² – b²) = 0 (CBSE 2012)

Or

Solve for x: 3x² – 2√6 x + 2 = 0 (CBSE 2012)

We have

4x² – 4ax + (a² – b²) = 0

Or 4x² – 4ax + a² – b² = 0

⇒ [(2x)² – 2(2x)(a) + (a)²] – b² = 0

⇒ (2x – a)² – b² = 0 [∵, a² – 2ab + b² = (a – b)²]

⇒ (2x – a + b)(2x – a – b) = 0 [∵, a² – b² = (a + b) (a – b)]

⇒ 2x – a + b = 0 or 2x – a – b = 0

⇒ 2x = a – b or 2x = a + b

⇒ x = (a – b)/2 or x = (a + b)/2

Hence, x = (a – b)/2 or x = (a + b)/2

Or

3x² – 2√6x + 2 = 0

⇒ 3x² – √6x – √6 + 2 = 0

⇒ √3√3x²– √3√2x – √3√2x + √2√2 = 0

⇒ √3x (√3x – √2) – √2 (√3x – √2) = 0

⇒ (√3x – √2) (√3x – √2) = 0

⇒ √3x – √2 = 0 or √3x – √2 = 0

⇒ x = √2/√3 or x = √2/√3

⇒ x = or x =

⇒ x = or x =

Hence, x = √6/3.