Question

10. Determine as raízes reais das equações incompletas: a) x2 − 6x = 0 b) −2x2 − 42x = 0 c) 5x2 + 20x = 0 d) x2 − 7x = 0 e) 10x2 − 90 = 0 f) 25x2 − 1 = 0 g) x2 − 64 = 0 h) x2 + 16 = 0 i) −7x2 + 28 = 0 j) (x − 7)(x − 3) + 10x = 30 k) 2x(x + 1) = x(x + 5) + 3(12 − x)

Answer 1

Oie, Td Bom?!

a)

$x {}^{2} - 6x = 0$

$x \: . \: (x - 6) = 0$

• $x = 0$

• $x - 6 = 0⇒x = 6$

$S = \left \{ 0 \: , \: 6\right \}$

b)

$- 2x {}^{2} - 42x = 0$

$- 2x \: . \: (x + 21) = 0$

$x \: . \: (x + 21) = 0$

• $x = 0$

• $x + 21 = 0⇒ x = - 21$

$S = \left \{ - 21 \: , \: 0 \right \}$

c)

$5x {}^{2} + 20x = 0$

$5x \: . \: (x + 4) = 0$

$x \: . \: (x + 4) = 0$

• $x = 0$

• $x + 4 = 0⇒x = - 4$

$S = \left \{ - 4 \: , \: 0 \right \}$

d)

$x {}^{2} - 7x = 0$

$x \: . \: (x - 7) = 0$

• $x = 0$

• $x - 7 = 0⇒x = 7$

$S = \left \{ 0 \: , \: 7\right \}$

e)

$10x {}^{2} - 90 = 0$

$x {}^{2} - 9 = 0$

$x {}^{2} = 9$

$x = ± \sqrt{9}$

$x = ±3$

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

f)

$25x {}^{2} - 1 = 0$

$25x {}^{2} = 1$

$x {}^{2} = \frac{1}{25}$

$x = ± \sqrt{ \frac{1}{25} }$

$x = ± \frac{1}{5}$

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

g)

$x {}^{2} - 64 = 0$

$x {}^{2} = 64$

$x = ± \sqrt{64}$

$x = ±8$

$S = \left \{ - 8 \: , \: 8 \right \}$

h)

$x {}^{2} + 16 = 0$

$x {}^{2} = - 16$

$x = ± \sqrt{ - 16}$

$x∉\mathbb{R}$

• A raiz quadrada do número negativo não pertence ao intervalo dos Números Reais.

i)

$- 7x {}^{2} + 28 = 0$

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

$x {}^{2} = 4$

$x = ± \sqrt{4}$

$x = ±2$

$S = \left \{ - 2 \: ,\: 2\right \}$

j)

$(x - 7) \: . \: (x - 3) + 10x = 30$

$x {}^{2} - 3x - 7x + 21 + 10x = 30$

$x {}^{2} + 0 + 21 = 30$

$x {}^{2} + 21 = 30$

$x {}^{2} = 30 - 21$

$x {}^{2} = 9$

$x = ± \sqrt{9}$

$x = ±3$

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

k)

$2x \: . \: (x + 1) = x \: . \: (x + 5) + 3(12 - x)$

$2x {}^{2} + 2x = x {}^{2} + 5x + 36 - 3x$

$2x {}^{2} + 2x = x {}^{2} + 2x + 36$

$2x {}^{2} = x {}^{2} + 36$

$2x {}^{2} - x {}^{2} = 36$

$x {}^{2} = 36$

$x = ± \sqrt{36}$

$x = ±6$

$S = \left \{ - 6 \: , \: 6 \right \}$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

x² - 6x = 0

x.(x - 6) = 0

• x' = 0

• x - 6 = 0

x" = 6

b)

-2x² - 42x = 0

2x² + 42x = 0

2x.(x + 21) = 0

• 2x = 0

x = 0/2

x' = 0

• x + 21 = 0

x" = -21

c)

5x² + 20x = 0

5x.(x + 4) = 0

• 5x = 0

x = 0/5

x' = 0

• x + 4 = 0

x" = -4

d)

x² - 7x = 0

x.(x - 7) = 0

• x' = 0

• x - 7 = 0

x" = 7

e)

10x² - 90 = 0

10x² = 90

x² = 90/10

x² = 9

x = ±√9

• x' = 3

• x" = -3

f)

25x² - 1 = 0

25x² = 1

x² = 1/25

x = ±√1/25

x' = 1/5

x" = -1/5

g)

x² - 64 = 0

x² = 64

x = ±√64

• x' = 8

• x" = -8

h)

x² + 16 = 0

x² = -16

Não há raízes reais

i)

-7x² + 28 = 0

7x² = 28

x² = 28/7

x² = 4

x = ±√4

• x' = 2

• x" = -2

j)

(x - 7).(x - 3) + 10x = 30

x² - 10x + 21 + 10x = 30

x² = 9

x = ±√9

• x' = 3

• x" = -3

k)

2x.(x + 1) = x.(x + 5) + 3.(12 - x)

2x² + 2x = x² + 5x + 36 - 3x

x² = 36

x = ±√36

• x' = 6

• x" = -6