Question

solve by using quadratic formula :-

Answer 1

9x² - 9(a + b)x + (2a² + 5ab + 2b²)
a = 9
b = -9(a + b) = -9a - 9b
c = 2a² + 5ab + 2b²

x1, 2
= [-b ± √(b² - 4ac)]/(2a)
= [-(-9a - 9b) ± √{(-9a - 9b)² - 4 . 9 . (2a² + 5ab + 2b²)}]/(2 . 9)
= [(9a + 9b) ± √{(81a² + 162ab + 81b²) - (72a² + 180ab + 72b²)}]/18
= [(9a + 9b) ± √(81a² - 72a² + 162ab - 180ab + 81b² - 72b²)]/18
= [(9a + 9b) ± √(9a² - 18ab + 9b²)]/18
= [(9a + 9b) ± √{9(a² - 2ab + b²)}]/18
= [(9a + 9b) ± √{9(a - b)²}]/18
= [(9a + 9b) ± 3(a - b)]/18

x1 = [(9a + 9b) + 3(a - b)]/18
x1 = (9a + 9b + 3a - 3b)/18
x1 = (12a + 6b)/18
x1 = 2/3a + 1/3b

x2 = [(9a + 9b) - 3(a - b)]/18
x2 = (9a + 9b - 3a + 3b)/18
x2 = (6a + 12b)/18
x2 = 1/3a + 2/3b