Question

Resolva a equação (determinante):
|1-x 1 1|
|1 1-x 1| = 0
|1 1 1-x|

Answer 1

$\left|\begin{array}{ccc}1-x&1&1\\1&1-x&1\\1&1&1-x\end{array}\right| =0\\ \\ \\ \left|\begin{array}{ccc}1-x&1&1\\1&1-x&1\\1&1&1-x\end{array}\right|\begin{array}{cc}1-x&1\\1&1-x\\1&1\end{array} =0\\ \\ \\ \\(1-x)\cdot(1-x)\cdot(1-x)+1\cdot1\cdot1+1\cdot1\cdot1\\-1\cdot(1-x)\cdot1-1\cdot1\cdot(1-x)-(1-x)\cdot1\cdot1=0\\ \\(1-x)^3+1+1-(1-x)-(1-x)-(1-x)=0\\ \\1-3x+3x^2-x^3+1+1-1+x-1+x-1+x=0 \\-x^3+3x^2-3x+x+x+x+1+1+1-1-1-1=0 \\-x^3+3x^2=0 \ \ (:x^2 \Longrightarrow x'=x''=0)\\ \\-x+3=0$
$\\-x=-3\\ \\x=\frac{-3}{-1}\\ \\x=3$
Logo, x = 0 u x = 3

Answer 2

Resposta:

x = 0   u x = 3

Explicação passo-a-passo: