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aflati coordonatele punctelor de intersectie dintre dereapta d: y=2x+1 si parabola P: y=x^2 +x+1

Răspuns :

[tex]d:y=2x+1[/tex]

[tex]P:y = {x}^{2} + x + 1[/tex]

[tex]2x + 1 = {x}^{2} + x + 1[/tex]

[tex] {x}^{2} + x - 2x + 1 - 1 = 0[/tex]

[tex] {x}^{2} - x = 0[/tex]

[tex]x(x - 1) = 0[/tex]

[tex]x_{1}=0 = > y_{1}=2 \times 0 + 1 = 1 = > A(0,1)[/tex]

[tex]x - 1 = 0 = > x_{2} = 1 = > y_{2} = 2 \times 1 + 1 = 3 = > B(1,3)[/tex]