4) Resolva as seguintes equações do 2º grau, sendo U = R :
a) x ^ 2 - 7x = 0
b) 4x ^ 2 - 9x = 0
c) x ^ 2 + x(x - 6) = 0
d) x(x - 3) - 2(x - 3) = 6
e) x ^ 2 + x = 0
f) 2x ^ 2 = 7x
g)(x+5)^ 2 =25
h) (x + 1)(x - 3) = - 3
Soluções para a tarefa
a) x ^ 2 - 7x = 0
x (x + 7) = 0
→ x¹ = 0
→ x + 7 = 0 ⨠ x² = -7
▶ S = {0, -7}
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b) 4x ^ 2 - 9x = 0
x (4x - 9) = 0
→ x¹ = 0
→ 4x - 9 = 0 ⨠ 4x = 9 ⨠ x² = 9/4
▶ S = {0, 9/4)
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c) x ^ 2 + x(x - 6) = 0
x² + x² - 6x = 0
2x² - 6x = 0
x (2x - 6) = 0
→ x¹ = 0
→ 2x - 6 = 0 ⨠ 2x = 6 ⨠ x² = 3
▶ S = {0, 3}
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d) x(x - 3) - 2(x - 3) = 6
x² - 3x -2x +6 = 6
x² - x = 0
x (x - 1) = 0
→ x¹ = 0
→ x - 1 = 0 ⨠ x² = 1
▶ S = {0, 1}
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e) x ^ 2 + x = 0
x (x + 1) = 0
→ x¹ = 0
→ x + 1 = 0 ⨠ x² = -1
▶ S = {0. -1}
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f) 2x ^ 2 = 7x
2x² - 7x = 0
x (2x - 7) = 0
→ x¹ = 0
→ 2x - 7 = 0 ⨠ 2x = 7 ⨠ x² = 7/2
▶ S = {0, 7/2}
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g)(x+5)^ 2 =25
x² + 10x + 25 = 25
x² + 10x = 0
x (x + 10) = 0
→ x¹ = 0
→ x + 10 = 0 ⨠ x² = -10
▶ S = {0, -10}
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h) (x + 1)(x - 3) = - 3
x² - 3x +x -3 = -3
x² - 2x = 0
x (x - 2) = 0
→ x¹ = 0
→ x - 2 = 0 ⨠ x² = 2
▶ S = {0, 2}
Resposta:
a) x² - 7x = 0
x(x-7)=0
x=0
x-7=0
x=7
S={0,7}
b) 4x² - 9x = 0
x(4x-9)=0
x=0
4x-9=0
4x=9
x=9/4
S={0,9/4}
c) x² + x(x - 6) = 0
x² +x²-6x=0
2x²-6x=0
x(2x-6)=0
x=0
2x-6=0
2x=6
x=6/2
x=3
s={0,3}
d) x(x - 3) - 2(x - 3) = 6
x²-3x-2x+6=6
x²-5x+6-6=0
x²-5x=0
x(x-5)=0
x=0
x-5=0
x=5
S={0,5}
e) x² + x = 0
x(x+1)=0
x=0
x+1=0
x=-1
S={-1,0}
f) 2x² = 7x
2x²- 7x=0
x(2x-7)=0
x=0
2x-7=0
2x=7
x=7/2
s={0,7/2}
g)(x+5)² =25
(x+5).(x+5)=25
x(x+5)+5(x+5)=25
x²+5x+5x+25=25
x²+10x+25-25=0
x²+10x=0
x(x+10)=0
x=0
x+10=0
x=-10
S={-10,0}
h) (x + 1)(x - 3) = - 3
x²-3x+x-3=-3
x²-2x-3+3=0
x²-2x=0
x(x-2)=0
x=0
x-2=0
x=2
S={0,2}
Explicação passo a passo: