Resolva as inequações:
a) (x –4).(x–2) > 0 d) 5x+10x- 3 < 0
b) (2x + 1) . (x + 2) ≤ 0.
c) (– x – 1) ⋅ (2x + 5) ≥ 0
Soluções para a tarefa
Resposta:
a) x'>+4; x".+2
b)x'≤+1/2 e x"≤-2
c) x'≥ +5/2; x"≥ +1
d) x<+1/5
Explicação passo-a-passo:
a) (x –4).(x–2) > 0
x^2-6x+8>0
Δ=b^2-4ac
Δ=(-6)^2-4*1*8
Δ=236-32
Δ=4
x'>(-(-6)+2/2
x'>(6+2)/2
x'=+4
x">(-(-6)-2)/2
x"=(6-2)/2
x">4/2
x"=+2
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b)(2x + 1) . (x + 2) ≤ 0
2x^2+3x+2≤ 0
Δ=3^2+4*2*2
Δ=9+16
Δ=25
x'≤-(+3)+5/4
x'≤-3+5/4
x'≤2/4
x'≤+1/2
x"≤-(3)-5/4
x"≤-8/4
x"≤-2
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c)(– x – 1) ⋅ (2x + 5) ≥ 0
-2x^2-7x-5 ≥0
Δ=49-4*(-2)*(-5)
Δ=49-40
Δ=9
x'≥ 7+3/4
x'≥+ 10/4
x'≥ 5/2
x"≥ 7-3/4
x"≥ 4/4
x"≥ +1
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d) 5x+10x- 3 < 0
15x-3<0
15x<3
x<3/15
x<+1/5
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