Question

Resolva as equações completas no conjunto R
A) X2 -8 +8X +15 = 0
B) X2 + 2X +1 =0
C) X2 -1X -2 = 0

Answer 1

Resolva as equações completas no conjunto R

A) x²- 8 + 8x +15 = 0

x² + 8x + 7 = 0

a = 1

b = 8

c = 7

∆ = b² - 4ac

∆ = 8² - 4 · 1 · 7

∆ = 64 - 28

∆ = 36

x = - b ± √∆ /2a

x = - 8 ± √36 /2 · 1

x = - 8 ± 6 /2

x¹ = - 8 + 6/2 = - 2/2 = - 1

x² = - 8 - 6/2 = - 14/2 = - 7

S = {- 7, - 1}

B) x² + 2x + 1 = 0

a = 1

b = 2

c = 1

∆ = b² - 4ac

∆ = 2² - 4 · 1 · 1

∆ = 4 - 4

∆ = 0

x = - b ± √∆ /2a

x = - 2 ± √0 /2 · 1

x = - 2 ± 0 /2

x¹ = - 2 + 0/2 = - 2/2 = - 1

x² = - 2 - 0/2 = - 2/2 = - 1

S = {- 1}

C) x² - 1x - 2 = 0

a = 1

b = (- 1)

c = (- 2)

∆ = b² - 4ac

∆ = (- 1)² - 4 · 1 · (- 2)

∆ = 1 + 8

∆ = 9

x = - b ± √∆ /2a

x = - (- 1) ± √9 /2 · 1

x = 1 ± 3 /2

x¹ = 1 + 3/2 = 4/2 = 2

x² = 1 - 3/2 = - 2/2 = - 1

S = {- 1, 2}

Espero ter ajudado! :)