Question

Solve the following equation by using formula :

4x² – 4ax + (a² – b²) = 0

Answer 1

4x² – 4ax + (a² – b²) = 0
Here a = 4, b = -4a, c = a² - b²
D = b² - 4ac
= (-4a)² - 4 x 4(a² - b²)
= 16a² - 16(a² - b²)
= 16a² - 16a² + 16b²
D = 16b² 

∵ x = `(-b ± sqrt("D"))/(2a)`

= `(-(-4a) ± sqrt(16b^2))/(2 xx 4)`

= `(4a ± 4b)/(8)`

= `(a + b)/(2)`

∴ `x_1 = (a + b)/(2), x_2 = (a - b)/(2)`

Hence x = `(a + b)/(2), (a - b)/(2)`.