Question

решите уравнение( (х-1)! /(х-3)! ) - (х! /(1! (х-1)!)=98

Answer 1

$frac{(x-1)!}{(x-3)!}- frac{x!}{1!(x-1)!} =98$

$frac{1cdot 2cdotdots (x-3)cdot(x-2)cdot(x-1)}{1cdot 2cdotdots (x-3)}- frac{1cdot 2cdot...cdot(x-1)cdot x}{1cdot 1cdot 2cdot...cdot(x-1)} =98$

$(x-2)(x-1)-x=98$
$x^2-4x-96=0$
$D=400$

$x_1= frac{4+20}{2} =12$

$x_1= frac{4-20}{2} =-8$