Question

решить уравнение.......

Answer 1

$frac{2x-3}{x-2} = 2x-7$
$frac{2x-3}{x-2} - (2x - 7) = 0$
$frac{2x-3}{x-2} - frac{(2x-7)(x-2)}{x-2} = 0$
$frac{2x-3}{x-2} - frac{2x^2-11x+14}{x-2} = 0$
$frac{2x-3-2x^2+11x-14}{x-2} = 0$
$frac{-2x^2+13x-17}{x-2} = 0$
$left { {{-2x^2+13x-17 = 0} atop {x-2 neq 0}} right.$
Решим квадратное уравнение:
$-2x^2+13x-17 = 0$
$2x^2-13x+17 = 0$
$D = b^2-4ac=169-4*2*17=33$
$x_{1} = frac{-b+ sqrt{D} }{2a} = frac{13+ sqrt{33} }{4}$
$x_{2} = frac{-b- sqrt{D} }{2a} = frac{13- sqrt{33} }{4}$
$left { {{x=frac{13 pm sqrt{33} }{4}} atop {x neq 2}} right.$
$x = frac{13 pm sqrt{33} }{4}$