Question

valor de x na expressão abaixo é:

2 pontos


15

12

4

6

​

Answer 1

Resposta:

6

Explicação passo-a-passo:

$\sf 2\cdot C_{x,2}=30$

$\sf 2\cdot\dfrac{x!}{(x-2)!\cdot2!}=30$

$\sf \dfrac{x\cdot(x-1)\cdot(x-2)!}{(x-2)!}=30$

$\sf x\cdot(x-1)=30$

$\sf x^2-x-30=0$

$\sf \Delta=(-1)^2-4\cdot1\cdot(-30)$

$\sf \Delta=1+120$

$\sf \Delta=121$

$\sf x=\dfrac{-(-1)\pm\sqrt{121}}{2\cdot1}=\dfrac{1\pm11}{2}$

$\sf x'=\dfrac{1+11}{2}~\longrightarrow~x'=\dfrac{12}{2}~\longrightarrow~x'=6$

$\sf x"=\dfrac{1-11}{2}~\longrightarrow~x"=\dfrac{-10}{2}~\longrightarrow~x"=-5$ (não serve)

$\sf S=\{6\}$