Question

x!-4.(x-1)!/(x-2)=10

Answer 1

Resposta:

X = -1 ou x = 6

Explicação passo-a-passo:

$\frac{x!-4(x-1)!}{(x-2)!}=10\\\\\frac{x(x-1)(x-2)!-4(x-1)(x-2)!}{(x-2)!}=10\\\\\frac{(x-2)![(x(x-1)-4(x-1)]}{(x-2)!}=10\\\\x(x-1)-4(x-1)=10\\\\x^{2}-x-4x+4-10=0\\\\x^{2}-5x-6=0\\\\D=(-5)^{2}-4.1(-6)\\\\D=25+24=49\\\\x=\frac{-(-5)-7}{2}=\frac{-2}{2}=-1\?ou\\\\x=\frac{-(-5)+7}{2}=\frac{5+7}{2}=\frac{12}{2}=6$