Bună! ⭐
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a) x²-x= 4 ⇔ x²-x-4= 0
a= 1; b= -1; c= -4
Δ= b²-4ac= 1+16= 17
[tex]=> x_{1} =\frac{-b-\sqrt{delta} }{2a} =\frac{1-\sqrt{17} }{2}[/tex]
[tex]=> x_{2} =\frac{-b+\sqrt{delta} }{2a} =\frac{1+\sqrt{17} }{2}[/tex]
x₁, x₂ ∉ Z ⇒ S=∅
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b) x³-x²= 100 ⇔ x³-x²-100= 0 ⇔
⇔ x³-5x²+4x²-100= 0 ⇔
⇔ x²(x-5)+4(x²-25)= 0 ⇔
⇔ x²(x-5)+4(x-5)(x+5)= 0 ⇔
⇔ (x-5)×[x²+4(x+5)]= 0 ⇔
⇔ (x-5)×(x²+4x+20)= 0 ⇔
x-5= 0 ⇒ x₁= 5 ∈ Z
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x²+4x+20= 0
a= 1; b= 4; c= 20
Δ= b²-4ac= 16-80= -64 ∉ R ⇒ x₂, x₃ ∉ Z
S={5}
#copaceibrainly
