Explicație pas cu pas:
f ∩ g => f(x) = g(x)
[tex]{x}^{2} + 2x - 1 = 5x + 3[/tex]
[tex]{x}^{2} - 3x - 4 = 0[/tex]
[tex](x + 1)(x - 4) = 0[/tex]
[tex]x + 1 = 0 \implies x = - 1 \\ y = 5( - 1) + 3 = - 5 + 3 \implies y = - 2 \\\implies P(-1;-2)[/tex]
[tex]x - 4 = 0 \implies x = 4 \\ y = 5 \times 4 + 3 = 20 + 3 \implies y = 23 \\\implies Q(4;23)[/tex]
[tex]PQ = \sqrt{ {(4 - ( - 1))}^{2} + {(23 - ( - 2))}^{2} } = \\ = \sqrt{ {5}^{2} + {25}^{2} } = \sqrt{25 + 625} = \sqrt{650} = \bf 5 \sqrt{26}[/tex]
