Question

Resolva as equações

(obs: cálculos)

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Answer 1

Resposta:

As respostas estão em negrito.

Explicação passo a passo:

a) ( x + 6) . (x - 6) = 0

x² - 6x + 6x - 36 = 0

x² - 36 = 0

x² = 36

x = +/- √36

x = +/- 6

b) (7x + 2) . (4x + 12) = 0

28x² + 54x + 8x + 24 = 0  (simplificando)

14x² + 27 x + 4x + 12 = 0

14x² + 31x + 12 = 0

Resolvendo pela fórmula de bhaskara:

a = 14  | b = 31  | c = 12

$\frac{-31 +/- \sqrt{31^{2} - 4 . 14 . 12 } }{2.14} \\\\\frac{-31+/- \sqrt{961-4. 168} }{28}\\\\\frac{-31+/-\sqrt{961 - 672} }{28}\\\\\frac{-31+/- \sqrt{289} }{28}\\\\\frac{-31+/- 17}{28} \\\\x' = \frac{-31 + 17}{28} = \frac{-14}{28} = \frac{-1}{2} \\\\x" = \frac{-31-17}{28} = \frac{-48}{28} = \frac{-12}{7}$

(-1/2 , -12/7)

c) 7y . ( 2y - 8) = 0

14y² - 56 = 0  (simplificando)

y² - 4 = 0

y² = 4

y = +/- √4

y = +/- 2

d) (x - 6) . (3x + 12) . (2x + 6) = 0

x - 6 = 0  

x = 6

3x + 12 = 0

3x = -12

x = -12/3

x = -4

2x + 6 = 0

2x = -6

x = -6/2

x = -3

e) (2x + 4) . (2x + 16) = 0

4x² + 32x + 8x + 64 = 0

4x² + 40x + 64 = 0  (simplificando)

x² + 10x + 16 = 0

Resolvendo pela fórmula de bhaskara:

a = 1  | b = 10  | c = 16

$\frac{-10+/- \sqrt{10^{2} - 4 . 1 .16 } }{2.1} \\\\\frac{-10+/- \sqrt{100 - 4 .16} }{2}\\\\\frac{-10 +/- \sqrt{100- 64} }{2}\\\\\frac{-10+/- \sqrt{36} }{2}\\\\\frac{-10+/- 6}{2}\\\\x' = \frac{-10+ 6}{2} = \frac{-4}{2} = -2\\\\x" = \frac{-10-6}{2} = \frac{-16}{2} = -8$

(-2, -8)

f) 4y . (y + 7) = 0

4y² + 28y = 0 (simplificando)

y² + 7y = 0

Resolvendo pela fórmula de bhaskara:

a = 1  | b = 7  | c = 0

$\frac{-7 +/- \sqrt{7^{2} - 4 . 1 . 0 } }{2.1}\\\\\frac{-7 +/- \sqrt{49 - 0} }{2}\\\\\frac{-7 +/- \sqrt{49} }{2} \\\\\frac{-7 +/- 7}{2}\\\\x' = \frac{-7 + 7}{2} = \frac{0}{2} = 0\\\\x" = \frac{-7 - 7}{2} = \frac{-14}{2} = -7$

(0 , -7)

g) (2x + 10) . (2x - 8) . (2x + 4) = 0

2x + 10 = 0

2x = -10

x= -10/2

x = -5

2x - 8 = 0

2x = 8

x = 8/2

x = 4

2x + 4 = 0

2x = -4

x = -4/2

x = -2

BONS ESTUDOS!!!