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Resolva as equações:
|x 4 -2|
|x-1 x 1| = |x 3|
|1 x+1 3| | 2 1|
|x 0 1|
|2x x 2| =0
|3 2x x|


RESOLVENDO

Por Matriz e Determinantes:
\( \left[\begin{array}{ccc}x&4&-2\\x-1& x&1\\1& x+1&3\end{array}\right] = \left[\begin{array}{ccc}x&3\\2&1\end{array}\right] \)
\( \left[\begin{array}{ccc}x&4&-2\\ x-1& x&1\\1& x+1&3\end{array}\right] \left[\begin{array}{ccc}x&4\\ x-1& x\\1& x+1\end{array}\right] = \left[\begin{array}{ccc}x&3\\2&1\end{array}\right] \left|\begin{array}{ccc}x\\2\end{array}\right| \)
[(x. x. 3) + (4. 1. 1) + (-2.(x-1). 1)] - [(-2. x. 1) + (x. 1.(x + 1)) + (4.(x - 1). 3)] = (x. 1) - (3. 2)
[(3x²) + (4) + ((-2x + 2). 1)] - [(-2x + 2). 1)  + (x² + x) + ((4x - 4). 3)] = (x) - (6)
[3x² + 4 + (-2x + 2)] - [(-2x +2) + x² + x + (12x - 12)] = x -6
[3x² + 4 - 2x + 2] - [-2x + 2 + x² + x + 12x - 12] = x - 6
[3x² - 2x + 4 + 2] - [x² + - 2x + x + 12x + 2 - 10] = x - 6
3x² - 2x + 6 - x² - 11x + 10 = x - 6
3x² - x² - 2x - 11x + 6 + 10 = x - 6
2x² - 13x + 16 - x + 6 = 0
2x² - 13x - x + 16 + 6 =
2x² - 14x + 22 = 0  (dividindo tudo por 2)
x² - 7x + 11 = 0
a = 1
b = - 7
c = 11
Δ = b² - 4. a. c
Δ = (-7)² - 4.(1).(11)
Δ = 49 - 44
Δ = 5
x = \( \frac{-b \ +- \ \sqrt{Δ} }{2a} \)
x = \( \frac{-(-7) \ + - \ \sqrt{5} }{2 \. \ 1} \)
x’ = \( \frac{7 \ + \ \sqrt{5} }{2} \)
x’’ = \( \frac{7 \ - \ \sqrt{5} }{2} \)
S = {\( \frac{7 \ + \ \sqrt{5} }{2} \); \( \frac{7 \ - \ \sqrt{5} }{2} \)}
\( \left[\begin{array}{ccc}x&0&1\\2x& x&2\\3&2x& x\end{array}\right] \)
\( \left[\begin{array}{ccc}x&0&1\\2x& x&2\\3&2x& x\end{array}\right] \left[\begin{array}{ccc}x&0\\2x& x\\3&2x\end{array}\right] = 0 \)
[(x. x. x) + (0. 2. 3) + (1. 2x. x)] - [(1. x. 3) + (x. 2. 2x) + (0. 2x. x)] = 0
[x³ + 0 + 2x²] - [3x + 4x² + 0] = 0
[x³ + 2x²] - [3x + 4x²] = 0
x³ + 2x² - 3x + 4x² =
x³ + 2x² + 4x² - 3x = 0
x³ + 6x² - 3x = 0  (colocando o "x"  em evidência):
x. (x² + 6x - 3) = 0 (I)
x = \( \frac{0}{ x^{2} \ + \ 6x \ - \ 3} \)
x = 0
x² + 6x - 3 = \( \frac{0}{x} \) (II)
x² + 6x - 3 = 0
Δ = (6)² - 4. (1). (-3)
Δ = 36 +12
Δ = 48
\( x = \frac{-6 \ +- \ \sqrt{48} }{2. 1} \\ x = \frac{-6 \ +- \ \sqrt{2^{2}.2^{2}.3} }{2} \\ x = \frac{-6 \ +- \ 2. 2. \sqrt{3} }{2} \\ x = \frac{-6 \ +- \ 4 \sqrt{3} }{2} \)
\( x’ = \frac{-6 \ + \ 4 \sqrt{3} }{2} \\ x’ = \frac{-6}{2} \ + \ \frac{4 \sqrt{3}}{2} \\ x’ = -3 \ + \ 2 \sqrt{3} \)
\( x’’ = \frac{-6 \ - \ 4 \sqrt{3} }{2} \\ x’’ = \frac{-6}{2} \ - \ \frac{4 \sqrt{3}}{2} \\ x’’ = -3 \ - \ 2 \sqrt{3} \)
S = {-3 + 2√3; -3 - 2√3)



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