Question

1) Resolva as equações de 2º grau completas:

a) 3x2 +12x - 63=0
b) X- 5x - 374 = 0
c) X2-14x + 48= 0
d) x2 - 4x - 5 = 0

Me ajudem nessa pfvr - 9° série

Answer 1

Resposta:

a) x = -7 ou 3

b) x = -17 ou 22

c) x = 6 ou 8

d) x = -1 ou 5

Explicação passo-a-passo:

a) 3x² + 12x - 63 = 0

3( x² + 4x -21) = 0

x² + 4x - 21 = 0

x =( -4 ± √ 16 + 84)/2

x = (-4 ± √100)/2

x = (-4 ± 10)/2

x = {-7;3}

b) x² - 5x - 374 = 0

x = (5 ± √ 25 + 1496)/2

x = (5 ± √ 1521)/2

x = (5 ± 39)/2

x = {-17;22}

c) x² - 14x + 48 = 0

x = (14 ± √196 - 192)/2

x = (14 ± √4)/2

x = (14 ± 2)/2

x = {6; 8}

d) x² - 4x - 5 = 0

x = (4 ± √ 16 + 20)/2

x = (4 ± √36)/2

x = (4 ± 6)/2

x = {-1; 5}

Answer 2

Oie, tudo bom?

a)

$3x {}^{2} + 12x - 63 = 0 \\ \frac{3x {}^{2} + 12x - 63 }{3} = 0 \\ x {}^{2} + 4x - 21 = 0$

$\boxed{a = 1 \: ,\: b = 4 \: ,\: c = - 12}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} \\ x = \frac{ - 4± \sqrt{4 {}^{2} - 4 \: . \: 1 \: . \: ( - 21) } }{2 \: . \: 1} \\ x = \frac{ - 4± \sqrt{16 + 84} }{2} \\ x = \frac{ - 4± \sqrt{100} }{2} \\ x = \frac{ - 4±10}{2} \\ x = \frac{ - 4 + 10}{2} = \frac{6}{2} = \boxed{3} \\ x = \frac{ - 4 - 10}{2} = \frac{ - 14}{2} = \boxed{ - 7}$

$\boxed{S = \left \{ - 7\: , \:3\right \}}$

b)

$x {}^{2} - 5x - 374 = 0$

$\boxed{a = 1 \: , \: b = - 5 \: ,\: c = - 374}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac} }{2a} \\ x = \frac{ - ( - 5)± \sqrt{( - 5) {}^{2} - 4 \: . \: 1 \: . \: ( - 374)} }{2 \: . \: 1} \\ x = \frac{5± \sqrt{25 + 1496} }{2} \\ x = \frac{5± \sqrt{1521} }{2} \\ x = \frac{5 ±39}{2} \\ x = \frac{5 + 39}{2} = \frac{44}{2} = \boxed{22} \\ x = \frac{5 - 39}{2} = \frac{ - 34}{2} = \boxed{ - 17}$

$\boxed{S = \left \{ - 17\: ,\:22\right \}}$

c)

$x {}^{2} - 14x + 48 = 0$

$\boxed{a = 1 \: , \: b = - 14 \: ,\: c = 48}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 14)± \sqrt{( - 14) {}^{2} - 4 \: . \: 1 \: . \: 48 } }{2 \: . \: 1} \\ x = \frac{14± \sqrt{196 - 192} }{2} \\ x = \frac{14± \sqrt{4} }{2} \\ x = \frac{14 ± 2}{2} \\ x = \frac{14 + 2}{2} = \frac{16}{2} = \boxed{8} \\ x = \frac{14 - 2}{2} = \frac{12}{2} = \boxed{6}$

$\boxed{S = \left \{8\: ,\:6\right \}}$

d)

$x {}^{2} - 4x - 5 = 0$

$\boxed{a = 1 \: ,\: b = - 4 \: , \: c = - 5}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac} }{2a} \\ x = \frac{ - ( - 4)± \sqrt{( - 4) {}^{2} - 4 \: . \: 1 \: . \: ( - 5) } }{2 \: . \: 1} \\ x = \frac{4± \sqrt{16 + 20} }{2} \\ x = \frac{4± \sqrt{36} }{2} \\ x = \frac{4±6}{2} \\ x = \frac{4 +6 }{2} = \frac{10}{2} = \boxed{5} \\ x = \frac{4 - 6}{2} = \frac{ - 2}{2} = \boxed{ - 1}$

$\boxed{S = \left \{ - 1\: ,\:5\right \}}$

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