Bună! ⭐
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Să se rezolve în mulțimea numerelor întregi ecuațiile:
b) x² + 2(x-4) = 3x - 8
f) (x+2)² - 3(x-1)² = 9
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[tex]b)[/tex] [tex]x^{2} +2(x-4)=3x-8 <=>[/tex]
[tex]<=> x^{2} +2x-8=3x-8 <=>[/tex]
[tex]<=> x^{2} +2x-8-3x+8=0 <=>[/tex]
[tex]<=> x^{2} -x=0 <=>[/tex]
[tex]<=> x(x-1)=0[/tex]
[tex]{\bold{CAZ_{1} : }[/tex] [tex]{\boxed{x=0}}[/tex] ∈ Z
[tex]{\bold{CAZ_{2} :}[/tex] [tex]x-1=0 => {\boxed{x=1}[/tex] ∈ Z
[tex]c)[/tex] [tex](x+2)^{2} -3(x-1)^{2} =9 <=>[/tex]
[tex]<=> x^{2} +4x+4-3(x^{2} -2x+1)=9 <=>[/tex]
[tex]<=> x^{2} +4x+4-3x^{2} +6x-3-9=0<=>[/tex]
[tex]<=> -2x^{2} +10x-8=0 /:(-2)<=>[/tex]
[tex]<=> x^{2} -5x+4=0[/tex]
[tex]a=1; b=-5; c=4[/tex]
[tex]delta=b^{2} -4ac = 25-16=9[/tex] [tex]>0[/tex]
[tex]=> x_{1} =\frac{-b-\sqrt{delta} }{2a} =\frac{5-3}{2} =\frac{2}{2} =1 => {\boxed{x_{1} =1}[/tex] ∈ Z
[tex]=> x_{2} =\frac{-b+\sqrt{delta} }{2a} =\frac{5+3}{2} =\frac{8}{2} =4=> {\boxed{x_{2} =4}[/tex] ∈ Z
#copaceibrainly
