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

A) X²- 6x= 0

X ( x - 6) =0

X'= 0

X-6=0

X"= 6

S= {6,0}

B) -2x²- 42x= 0. (×-1)

2x²- 42x= 0

X(2x- 42)= 0

X'= 0

2x- 42=0

2x= 42

X= 42/2

X"= 21

S={21,0}

C) 5x²+ 20x = 0

X(5x+20)=0

X'= 0

5x= -20

X= -20/5

X"= -4

S={-4,0}

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

S= {+3,-3}

F) 25x²-1=0

25x²= 1

X= ±√1/25

X=  ± 1/5

S={±1/5}

G) X²-64=0

X²= 64

X= ±√64

X= ± 8

S= {8,-8}

H) X²+16=0

X²= -16

X= ±√-16

A EQUAÇÃO NÃO POSSUI RAIZ REAL.

I) −7x2 + 28 = 0

-7x²= -28. (×-1)

X²= 28/7

X²= 4

X= ±√4

X= ±2

S={±2}

J) (x − 7)(x − 3) + 10x = 30

X²- 3x- 7x + 21 + 10x= 30

X²- 3x- 7x + 10x= 30

X²- 10x+ 10x= 30

X²= 30

X= ±√30

S= { √30 , - √30}

K) 2x(x + 1) = x(x + 5) + 3(12 − x)

2x²+ 2x = x²+ 5x + 36- 3x

2x²- x²+ 2x - 5x + 3x= 36

X²- 3x+ 3x= 36

X²= 36

X= ±√36

X= ±6

S= { + 6 , - 6}

Espero ter ajudado :)

Answer 2

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