Question

please answer my question
no 9

Answer 1

9. taking LCM of (x - a) and (x - b) we get :

$\frac{a(x - a) + b(x - b)}{(x - a)(x - b)}$ = 2

cross multiplying we get :

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

⇒ 2x² - 3x(a +b) + (a +b)² = 0

take a + b = y

⇒ 2x² - 3x(y) + (y)² = 0

⇒ 2x² - 2xy - xy + y² = 0

⇒ 2x(x - y) - y(x - y) = 0

⇒ 2x - y = 0 or x - y = 0

⇒ x = $\frac{y}{2}$ or x = y

but y = a + b

⇒ x = $\frac{a + b}{2}$ or x = a + b