Question

Resolva a expressão : C x, 3   - 6. C x,2 = 0

Answer 1

$C_{x,3}-6C_{x,2}=0\\\\\\\dfrac{x!}{3!(x-3)!}-6\dfrac{x!}{2!(x-2)!}=0\\\\\\\dfrac{x(x-1)(x-2)(x-3)!}{3\cdot2(x-3)!}-6\dfrac{x(x-1)(x-2)!}{2(x-2)!}=0\\\\\\\dfrac{x(x-1)(x-2)}{6}-18\dfrac{x(x-1)}{6}=0\\\\\\\dfrac{x(x-1)(x-2)-18x(x-1)}{6}=0\\\\\\x(x-1)(x-2)-18x(x-1)=0$

Colocando x(x - 1) em evidência:

$x(x-1)\cdot(x-2-18)=0\\x(x-1)(x-20)=0$

Igualando cada parcela a zero:

$x=0\\\\x-1=0~~~~~~~~\therefore~~~~~~~~~~x=1\\\\x-20=0~~~~~~~\therefore~~~~~~~~x=20$

$\boxed{\boxed{S=\{0,1,20\}}}$