Question

200/x- 200 /x + 5 =2
Solve the following by quadratic​

Answer 1

Explanation:

$\frac{200}{x} - \frac{200}{x + 5} = 2$

$= > \frac{200(x + 5) - 200x}{x(x + 5)} = 2$

$= > \frac{200x + 1000 - 200x}{ {x}^{2} + 5x} = 2$

$= > 1000 = 2( {x}^{2} + 5x)$

$= > {x}^{2} + 5 x= \frac{1000}{2}$

$= > {x}^{2} + 5x = 500$

$= > {x}^{2} + 5x - 500 = 0$

$= > {x}^{2} + (25 - 20)x - 500 = 0$

$= > {x}^{2} + 25x - 20x - 500 = 0$

$= > x (x + 25) - 20(x + 25) = 0$

$= > (x + 25)(x - 20) = 0$

Either, x +25 =0 => x = - 25

Or, x-20=0 => x = 20

The two roots of the quadratic equation are 20 and -25.