Question

4x^2-4ax+(a^2-b^2)=0​

Answer 1

4x² - 4ax + (a² - b²) = 0, is $x = \frac{a - b}{2} ; x= \frac{a+b}{2}$

Explanation:

Given: 4x² - 4ax + (a² - b²) = 0

We know that a² - b² = (a - b) (a + b)

Substituting we get,

4x² - 4ax + (a - b) (a + b) = 0

⇒ 4x² + [- 2a - 2a + 2b - 2b]x + (a - b) (a + b) = 0

⇒ 4x² + (2b - 2a)x - (2a + 2b)x + (a - b) (a + b) = 0

⇒ 4x² + 2(b - a)x - 2(a + b)x + (a - b) (a + b) = 0

⇒2x [2x - (a - b)] - (a + b)[2x - (a - b)] = 0

⇒ [2x - (a - b)][2x - (a + b)] = 0

⇒ 2x − (a - b) = 0, 2x - (a + b) = 0

⇒ 2x = a - b; 2x = a + b

⇒ $x = \frac{a - b}{2} ; x= \frac{a+b}{2}$

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