Question

find x using quadratic equation​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x = \frac{2ab - ac - ab}{a - 2c + b}}}}$

Step-by-step explanation:

$\sf \frac{a}{x - a} + \frac{b}{x - b} = \frac{2c}{x - c}$

It can be written as ;

$\sf \implies \frac{a}{x - a} + \frac{b}{x - b} = \frac{c +c}{x - c}$

$\sf \implies \frac{a}{x - a} + \frac{b}{x - b} = \frac{c}{x - c} + \frac{c}{x - c}$

$\sf \implies \frac{a}{x - a} - \frac{c}{x - c} = \frac{c}{x - c} - \frac{b}{x - b}$

Now, taking LCM -

$\sf \implies \frac{a(x - c) - c(x - a)}{(x - a) \cancel{(x - c)}} = \frac{c(x - b) - b(x - c)}{ \cancel{(x - c)}(x - b)}$

$\sf \implies \frac{ax -ac - cx + ac}{x - a} = \frac{cx - cb - bx +bc }{x - b}$

$\sf \implies \frac{ax - cx}{x - a} = \frac{cx - bx}{x - b}$

$\sf \implies \frac{x(a - c) }{x - a} = \frac{x(c - b)}{x - b}$

$\sf \implies \frac{a - c}{x - a} = \frac{c - b}{x - b}$

$\sf \implies\small(a - c)(x - b) = (c - b)(x - a) \\ \\ \small \sf \implies ax - ab - cx + bc = cx - ac - bx + ab \\ \\ \bf Taking \: like \: terms \: one \: side - \\ \\ \sf \implies ax - cx - cx + bx = - ac + ab + ab - bc \\ \\ \sf \implies ax - 2cx + bx = 2ab - ac - ab \\ \\ \sf \implies x(a - 2c + b) = 2ab - ac - ab \\ \\ \red{\boxed{\bf x = \frac{2ab - ac - ab}{a - 2c + b} }} \rightarrow \sf Answer.$