Odpowiedź:
zad. 77
[tex]a) {x}^{2} - 7x + 12 = 0 \\ ∆ = {b}^{2} - 4ac = ( - 7 {)}^{2} - 4 \times 1 \times 12 = 49 - 48 = 1 \\ \sqrt{∆} = \sqrt{1} = 1 \\ x_{1} = \frac{ - b - \sqrt{∆} }{2a} = \frac{7 - 1}{2} = \frac{6}{2} = 3 \\ x_{2} = \frac{ - b + \sqrt{∆} }{2a} = \frac{7 + 1}{2} = \frac{8}{2} = 4[/tex]
zad. 78
[tex]a) 10 = 2.5x \times x \\ 10 = 2.5 {x}^{2} \\ {x}^{2} = 4 \\ x = 2 \\[/tex]
jeden bok x=2
drugi bok 2,5x=2,5×2=5
[tex]ob = 2 \times 2 + 2 \times 5 = 4 + 10 = 14[/tex]
zad. 79
[tex]p = {800m}^{2} [/tex]
[tex]ob = 120m[/tex]
[tex]xy = 800 \\ 2x + 2y = 120 \\ \\xy = 800 \\ x + y = 60 \\ \\ xy = 800 \\ x = 60 - y \\ \\ (60 - y)y = 800 \\ x = 60 - y \\ \\ 60y - {y}^{2} = 800 \\ - {y}^{2} + 60y - 800 = 0 \\ {y}^{2} - 20y - 40 y + 800 = 0 \\ y(y - 20) - 40(y - 20) = 0 \\(y - 20)(y - 40) = 0 \\ y_{1} = 20 \: \: \: y_{2}= 40[/tex]
[tex] x_{1} = 60 - 20 = 40 \\ x_{2} = 60 - 40 = 20[/tex]
