1)Resolva os sistemas de equação 2° grau:
a)�
+ = 6
= 8
b) �
− = −7
= 10
c) �
+ = 6
= −16
d) �
− = 3
= −2
e) �
2 − = 3
3 = 231
Respostas
Resposta:
a)
{ x+y=6
{ xy=8
t² - 6t + 8 = 0
a = 1
b = -6
c = 8
d² = 36 - 32 = 4
d = 2
t1 = (6 + 2)/2 = 8/2 = 4
t2 = (6 - 2)/2 = 4/2 = 2
x = 2, y = 4
x = 4, y = 2
b)
{x+y=-7
{xy=10
t² + 7t + 10 = 0
a = 1
b = 7
c = 10
d² = 49 - 40 = 9
d = 3
t1 = (-7 + 3)/2 = -4/2 = -2
t2 = (-7 - 3)/2 = -10/2 = -5
x = -5, y = -2
x = -2, y = -5
c)
{x+y=6
{xy=-16
t² - 6t - 16 = 0
a = 1
b = -6
c = -16
d² = 36 + 64 = 100
d = 10
t1 = (6 + 10)/2 = 16/2 = 8
t2 = (6 - 10)/2 = -4/2 = --2
x = -2. y = 8
x = 8, y = -2
d)
{x-y=3
{xy=-2
x*(x - 3) = -2
x² - 3x + 2 = 0
a = 1
b = -3
c = 2
d² = 9 - 8 = 1
d = 1
x1 = (3 + 1)/2 = 4/2 = 2
x2 = (3 - 1)/2 = 2/2 = 1
x1 = 2, y1 = -1
x2 = 1. y2 = -2
e)
{2x-y=3
{3xy=231
2x - y = 3
xy = 77
x*(2x - 3) = 77
2x² - 3x - 77 = 0
a = 2
b = -3
c = -77
d² = 9 + 8*77
d² = 625
d = 25
x1 = (3 + 25)/4 = 7 y1 = 2x - 3 = 11
x2 = (3 - 25)/4 = -11/2 .y2 = -11 - 3 = -14
Explicação passo a passo: