Question

Rezolvă ecuațiile:
Combinări de x luate cate 3 = 5/4 x(x-3)
5 Combinări de x luate câte 3 = combinari de x+2 luate cate 4

Answer 1

$\it C_x^3=\dfrac{5}{4}x(x-3) \Rightarrow \dfrac{x!}{3!(x-3)!}=\dfrac{5}{4}x(x-3)\Rightarrow\\ \\ \\ \Rightarrow \dfrac{(x-3)!(x-2)(x-1)x}{6(x-3)!}=\dfrac{5}{4}x(x-3)\Rightarrow \dfrac{(x-2)(x-1)}{6}= \dfrac{5x(x-3)}{4}|_{:x} \Rightarrow\\ \\ \\ \Rightarrow \dfrac{(x-2)(x-1)}{6}= \dfrac{5(x-3)}{4} \Rightarrow \dfrac{(x-2)(x-1)}{x-3}=\dfrac{30}{4} \Rightarrow x=7$