Question

19) Resolva as seguintes equações do 2º grau
a) x2 - 25 = 0
b) 2x - 32 = 0
c) 7x2 - 343 = 0
d) x2 - 81 = 0
) 2x2 - 50 = 0
e) x2 = 1
g) 7x? - 7 = 0
h) 5x2 - 15 = 0
1) 21 = 7x2
1) 5x2 + 20 = 0
k) 7x + 2 = 30
1) 2x2 - 90 = 8
m) 4x? - 27 = x
n) 8x2 = 60 - 7x​

Answer 1

Boa Noite !!!

Lembramos que quando um número passa ao outro lado inverte o sinal:

a) x² - 25 = 0

a) x = √25

a) x = 5

b) 2x² - 32 = 0

b) x² = 32/2

b) x² = 16

b) x = √16

b) x = 4

c) 7x² - 343

c) x² = 343/7

c) x² = 49

c) x = √49

c) x = 7

d) x² - 81

d) x = √81

d) x = 9

e) 2x² - 50 = 0

) x² = 50/2

) x² = 25

) x = √25

) x = 5

e) x² = 1

e) x = √1

e) x = 1

g) {7x} - 7 = 0

g) 7x = 7

g) x = 7/7

g) x = 1

h) 5x² - 15 = 0

h) 5x² = 15

h) x² = 15/5

h) x² = 3

h) x = √3

1) 21 = 7x²

1) 7x² = 21

1) x² = 21/7

1) x = √3 ou

1) x = 1,7320

1) 5x² + 20 = 0

1) x² = -20/5

1) x² = -4

1) x = ∉

k) 7x + 2 = 30

k) 7x = 30 - 2

k) 7x = 28

k) x = 28/7

k) x = 4

1) 2x² - 90 = 8

1) 2x² = 98

1) x² = 98/2

1) x² = 49

1) x = √49

1) x = 7

m) {4x} - 27 = x

m) 4x - x = 27

m) 3x = 27

m) x = 27/3

m) x = 9

n) 8 x 2 = 60 - 7x

n) 7x = 60 - 16

n) x = 44/7 ou

n) x = 6,2857

Answer 2

Resposta:

Explicação passo-a-passo:

a) x2 - 25 = 0  => x² = 25 => $x = \sqrt{25} => x = 5$ =>  x = ±5

b) 2x - 32 = 0  => 2x = 32 => x = $\frac{32}{2} = x = 16$

c) 7x2 - 343 = 0 => 7x² = 343 => $x^{2} = \frac{343}{7} => x^{2} = 49 => x=\sqrt{49} => x = 7$ => x = ±7

d) x2 - 81 = 0 => x² = 81=>  $x^{} =\sqrt{81} => x = 9$ => x = ±9

) 2x2 - 50 = 0  => 2x² = 50 => $x^{2} =\frac{50}{2} => x^{2} = 25=> x=\sqrt{25} => x= 5$=> x = ±5

e) x2 = 1 => $x^{2} =\sqrt{1}=> x = 1$ => x = ±1

g) 7x? - 7 = 0  => 7x = 7 => $x = \frac{7}{7} => x = 1$

h) 5x2 - 15 = 0 => 5x² = 15 =>x² = $\frac{15}{5} =>$ $x^{} =\sqrt{3}=>$ x = ± $\sqrt{3}$

1) 21 = 7x2  => -7x² = -21 => $x^{2} = \frac{-21}{-7} => x^{2} = 3=> x= \sqrt{3}$=> x = ± $\sqrt{3}$

1) 5x2 + 20 = 0  => 5x² = -20 => x² = $\frac{-20}{5} => x^{2} = -4$ ∉

k) 7x + 2 = 30  => 7x  = 30  - 2=> 7x  = 28=> x = $\frac{28}{7} = x = 4$

1) 2x2 - 90 = 8 => 2x² = 8 + 90 => 2x² = 98 => $\frac{x}{y} x^{2} =\frac{27}{2} => x^{2} = \frac{98}{2} => x^{2} = 49 => x^{}=\sqrt{49}=> x = 7$=> x = ±7

m) 4x? - 27 = x  => 4x - x = 27  => 3x = 27 => $x =\frac{27}{3} = x = 9$

n) 8x2 = 60 - 7x​ => 8x² + 7x -60 = 0​ => Δ= b² -4ac=> Δ= (7)² -4(8)(-60)=>

Δ= 49 + 1920=> Δ=  1969

x = -b±√Δ/2a =>x = -7±√1969/2(8) =>  $x_{1} = \frac{-7 + \sqrt{1969} }{16} \\x_{2} = \frac{-7 - \sqrt{1969} }{16}$