Question

1) Encontre as raízes das seguintes equações:
a) X² - 25 = 0

b) 2x² - 200 = 0

c) X² - 10 = 0

d) X² - 2x – 3 = 0

e) X² + 4x + 2 = 0

Answer 1

Explicação passo-a-passo:

a) X² - 25 = 0

X² = 25

X= ±5

B) 2X² - 200= 0

Divide por 2

X² - 100 = 0

X² = 100

X= ±10

C) X² - 10 = 0

X² = 10

X= ±√10

D) X= -(-2)±√4+12/2

X= 2±4/2

X= 3

X= -1

e) X²+4X +2= 0

X= -4±√16-8/2

X= -4±2√2/2

X= -2±√2

Answer 2

Resposta:

A)x2- 25 = 0

( 1 ) ⋅x2+ ( - 25 ) = 0

x =±- ( 1 ) ⋅ ( - 25 )-----------√1

x = ±25--√

x = ± ( 5 )

x1= 5

x2= - 5

B)2x2- 200 = 0

( 2 ) ⋅x2+ ( - 200 ) = 0

x =±- ( 2 ) ⋅ ( - 200 )------------√2

x =±400---√2

x =± ( 20 )2

x = ±( 2 )⋅ ( 10 )( 2 )

x1= 10

x2= - 10

C)x2- 10 = 0

( 1 ) ⋅x2+ ( - 10 ) = 0

x =±- ( 1 ) ⋅ ( - 10 )-----------√1

x = ±10--√

x1=10--√

x2= -10--√

D)x2- 2 x - 3 = 0

( 1 ) ⋅x2+ ( - 2 ) ⋅ x + ( - 3 ) = 0

x =- ( - 2 ) ±( - 2 )2- 4 ⋅ ( - 3 )---------------√2

x =2 ±4 - ( - 12 )---------√2

x =2 ±16--√2

x =2 ± ( 4 )2

x1=62=( 2 )⋅ ( 3 )( 2 )= 3

E)x2+ 4 x + 2 = 0

( 1 ) ⋅x2+ ( 4 ) ⋅ x + ( 2 ) = 0

x =- ( 4 ) ±( 4 )2- 4 ⋅ ( 2 )----------√2

x =- 4 ±16 - ( 8 )-------√2

x =- 4 ±8-√2

x =- 4 ± ( 2 ) ⋅2-√2

x =( 2 )⋅ [ ( - 2 ) ±2-√]( 2 )

x1= - 2 +2-√

x2= - 2 -2-√