Question

35.7. Найдите корни уравнения:
1) (х - 7)^2 - 49 =0;
3) 100 - (2-19)^2= 0;
2) (6 +y)^2- 81 =0;
4) 25 - (13 +t)^2=0.​

Answer 1

1)

$(x - 7 {)}^{2} - 49 = 0 \\ {x}^{2} - 14x + 49 - 49 = 0 \\ {x}^{2} - 14x = 0 \\ x(x - 14) =0 \\ x = 0 \: \: \: \: \: \: \: \: \: \: \: x - 14 = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 14 \\ \\ x1 = 0 \\ x2 = 14$

3) Ошибка в уравнении

2)

$(6 + y {)}^{2} - 81 = 0 \\ 36 + 12y + {y}^{2} - 81 = 0 \\ {y}^{2} + 12y - 45 = 0 \\ d = ( {12)}^{2} - 4 \times 1 \times ( - 45) = 144 + 180 = 324 \\ x1 = \frac{ - 12 + 18}{2} = \frac{6}{2} = 3 \\ x2 = \frac{ - 12 - 18}{2} = \frac{ - 30}{2} = - 15 \\ \\ x1 = 3 \\ x2 = - 15$