Question

1) Resolva as equações, usando a fórmula de Báskara :

a) x² - 7x + 10 = 0

b) x² - 8x + 16 = 0

c) x² - 13x = 0

d) x² - 25 = 0

e) x² - 4x + 9 = 0

f) 6x² + x - 1 = 0

Answer 1

Explicação passo-a-passo:

a)x² - 7x + 10 = 0

Δ=b²-4·a·c

Δ= (-7)²-4·1·10

Δ=49-40

Δ=9

x= -b±√Δ/2·a

x= -(-7)±√9/2·1

x= 7±3/2

x´1= 7-3/2⇒x´1=4/2⇒Resposta⇒2

x´2=7+3/2⇒x´1=10/2⇒Resposta⇒5

b)x² - 8x + 16 = 0

Δ=b²-4·a·c

Δ= (-8)²-4·1·16

Δ=64-64

Δ=0

x= -b±√Δ/2·a

x= -(-8)±√0/2·1

x= 8±0/2

x´1= 8-0/2⇒x´1= 8/2⇒Resposta⇒x´1=4

x´2= 8+0/2⇒Resposta⇒x´2=4

c)x² - 13x = 0

Δ=(-13)²-4·1·0

Δ=169-0

Δ=169

x=-(-13)±√169/2·1

x= 13±13/2

x´1= 13-13/2⇒Resposta⇒x´1=0/2

x´2= 13+13/2⇒Resposta⇒x´2=13

d)x² - 25 = 0

Δ= 0²-4·1·-25

Δ=100

x= 0±√100/2·1

x´1= 0-100/2⇒Resposta⇒x´1= -50

x´2=0+100/2⇒Resposta⇒x´2= 50

e)x² - 4x + 9 = 0

Δ= (-4)²-4·1·9

Δ=16-36

Δ= -20

f) 6x² + x - 1 = 0

Δ= 1²-4·6·-1

Δ=1+24

Δ=25

x=-1±√25/2·6

x= -1±5/12

x´1= -1-5/12⇒Resposta⇒x´1= -1/6

x´2= -1+5/12⇒Resposta⇒x´2= 1/3