Question

1/a+b+x - 1/x = 1/a + 1/b

solve quadratic equation​

Answer 1

Answer:

x = -a or, x = -b

Step-by-step explanation:

$\frac{1}{a+b+x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b}$

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

⇒ $\frac{-1}{x (a+b+x)} = \frac{1}{ab}$

⇒ -ab = x (a+b) + x²   ⇒ x² + (a+b)x + ab = 0

Discriminant, D = (a+b)² - 4ab = a² - 2ab + b² = (a-b)²

∴ Roots are ( -(a+b) ± √D )/2

x1 = [ - (a+b) + (a-b) ]/2 = -b

x2 = [ - (a+b) - (a-b) ]/2 = -a