Question

determine a solucao das seguintes eqacoes A) x² + x - 2 =0 B)x² + 8x + 15 =0 C) 2x² + 8x - 10 =0 D) y² - 10y + 24 =0

Answer 1

Explicação passo-a-passo:

Usaremos a fórmula de Bhaskara:

x = - b ± √b² - 4ac/2a

a) x² + x - 2 = 0

x = - 1 ± √1² - 4.1.(-2)/2.1

x = - 1 ± √1 + 8/2

x = - 1 ± √9/2

x = - 1 ± 3/2

x' = - 1+3/2 = 2/2 = 1

x' = - 1-3/2 = - 4/2 = - 2

S = {- 2 ; 1}

b) x² + 8x + 15 = 0

x = - 8 ± √8² - 4.1.15/2.1

x = - 8 ± √64 - 60/2

x = - 8 ± √4/2

x = - 8 ± 2/2

x' = - 8+2/2 = - 6/2 = - 3

x' = - 8-2/2 = - 10/2 = - 5

S = {- 5 ; - 3}

c) 2x² + 8x - 10 = 0

x = - 8 ± √8² - 4.2.(-10)/2.2

x = - 8 ± √64 + 80/4

x = - 8 ± √144/4

x = - 8 ± 12/4

x' = - 8+12/4 = 4/4 = 1

x' = - 8-12/4 = - 20/4 = - 5

S = {- 5 ; 1}

d) y² - 10y + 24 = 0

y = - (-10) ± √(-10)² - 4.1.24/2.1

y = 10 ± √100 - 96/2

y = 10 ± √4/2

y = 10 ± 2/2

y' = 10+2/2 = 12/2 = 6

y" = 10-2/2 = 8/2 = 4

S = {4 ; 6}