Question

ligue cada equação ao seu conjunto verdade x- 7x + 6 =0

x-X- 12=0

x? - 3x – 4 = 0

x - 4x + 4 = 0

V= {-3,4}

V= (2}

V= {1,6}

V = {-1, 4}​

Answer 1

Oie, Td Bom?!

1.

$x {}^{2} - 7x + 6 = 0 ⇒ V= \left \{ 1 \: , \: 6 \right \}$

• Coeficientes:

$a = 1 \: , \: b = - 7 \: , \: c = 6$

• Fórmula resolutiva:

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a}$

$x = \frac{ - ( - 7) {}^{2}± \sqrt{( - 7) {}^{2} - 4 \: . \: 1 \: . \: 6} }{2 \: . \: 1}$

$x = \frac{7± \sqrt{49 - 24} }{2}$

$x = \frac{7± \sqrt{25} }{2}$

$x = \frac{7±5}{2}$

$⇒x = \frac{7 + 5}{2} = \frac{12}{2} = 6$

$⇒x = \frac{7 - 5}{2} = \frac{2}{2} = 1$

2.

$x {}^{2} - x - 12 = 0 ⇒ V= \left \{ - 3 \: , \:4 \right \}$

• Coeficientes:

$a = 1 \: , \: b = - 1 \: ,\: c = - 12$

• Fórmula resolutiva:

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a}$

$x = \frac{ - ( - 1)± \sqrt{( - 1) {}^{2} - 4 \: . \: 1 \: . \: ( - 12) } }{2 \: . \: 1}$

$x = \frac{1± \sqrt{1 + 48} }{2}$

$x = \frac{1± \sqrt{49} }{2}$

$x = \frac{1±7}{2}$

$⇒x = \frac{1 + 7}{2} = \frac{8}{2} = 4$

$⇒x = \frac{ 1 - 7}{2} = \frac{ - 6}{2} = - 3$

3.

$x {}^{2} - 3x - 4 = 0⇒ V= \left \{ - 1 \: , \:4 \right \}$

• Coeficientes:

$a = 1 \: , \: b = - 3 \: ,\: c = - 4$

• Fórmula resolutiva:

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a}$

$x = \frac{ - ( - 3)± \sqrt{( - 3) {}^{2} - 4 \: . \: 1 \: . \: ( - 4)} }{2 \: . \: 1}$

$x = \frac{3± \sqrt{9 + 16} }{2}$

$x = \frac{3± \sqrt{25} }{2}$

$x = \frac{3±5}{2}$

$⇒x = \frac{3 + 5}{2} = \frac{8}{2} = 4$

$⇒x = \frac{3 - 5}{2} = \frac{ - 2}{2} = - 1$

4.

$x {}^{2} - 4x + 4 = 0⇒ V= \left \{ 2\right \}$

• Coeficientes:

$a = 1 \:, \: b = - 4 \: , \: c = 4$

• Fórmula resolutiva:

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac} }{2a}$

$x = \frac{ - ( - 4)± \sqrt{( - 4) {}^{2} - 4 \: . \: 1 \: . \: 4 } }{2 \: . \: 1}$

$x = \frac{4± \sqrt{16 - 16} }{2}$

$x = \frac{4± \sqrt{0} }{2}$

$x = \frac{4±0}{2}$

$x = \frac{4}{2}$

$x = 2$

Att. Makaveli1996