Question

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

Answer 1

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

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

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

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

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