LB 1. x^2 = 49 2. x^2 - 8x = 0 3. x^2 - 10x + 25 = 0 4. x^2 - 169 = 0 5. x^2 = 3x 6. x^2 + 8x = 9 7. x^2 = 16 8. (x-2)(-x-1) = 0 9. 7x^2 - 14x = 0 10. 2x^2 + 5x - 3 = 0 11. 4x^2 + 21 = 0 12. 3x^2 - 2x + 4 = 0

Решение:

1. \( x^2 = 49 \)
   \( x = \pm\sqrt{49} \)
   \( x = \pm7 \)
2. \( x^2 - 8x = 0 \)
   \( x(x - 8) = 0 \)
   \( x = 0 \) или \( x = 8 \)
3. \( x^2 - 10x + 25 = 0 \)
   \( (x - 5)^2 = 0 \)
   \( x = 5 \)
4. \( x^2 - 169 = 0 \)
   \( x^2 = 169 \)
   \( x = \pm\sqrt{169} \)
   \( x = \pm13 \)
5. \( x^2 = 3x \)
   \( x^2 - 3x = 0 \)
   \( x(x - 3) = 0 \)
   \( x = 0 \) или \( x = 3 \)
6. \( x^2 + 8x = 9 \)
   \( x^2 + 8x - 9 = 0 \)
   \( (x + 9)(x - 1) = 0 \)
   \( x = -9 \) или \( x = 1 \)
7. \( x^2 = 16 \)
   \( x = \pm\sqrt{16} \)
   \( x = \pm4 \)
8. \( (x - 2)(-x - 1) = 0 \)
   \( -x - 1 = 0 \) или \( x - 2 = 0 \)
   \( x = -1 \) или \( x = 2 \)
9. \( 7x^2 - 14x = 0 \)
   \( 7x(x - 2) = 0 \)
   \( x = 0 \) или \( x = 2 \)
10. \( 2x^2 + 5x - 3 = 0 \)
    \( D = 5^2 - 4(2)(-3) = 25 + 24 = 49 \)
    \( x = \frac{-5 \pm\sqrt{49}}{2(2)} = \frac{-5 \pm 7}{4} \)
    \( x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = 0.5 \)
    \( x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3 \)
11. \( 4x^2 + 21 = 0 \)
    \( 4x^2 = -21 \)
    \( x^2 = -21/4 \)
    Нет действительных решений.
12. \( 3x^2 - 2x + 4 = 0 \)
    \( D = (-2)^2 - 4(3)(4) = 4 - 48 = -44 \)
    Нет действительных решений.

Ответ: 1. \( x=\pm7 \); 2. \( x=0, x=8 \); 3. \( x=5 \); 4. \( x=\pm13 \); 5. \( x=0, x=3 \); 6. \( x=-9, x=1 \); 7. \( x=\pm4 \); 8. \( x=-1, x=2 \); 9. \( x=0, x=2 \); 10. \( x=0.5, x=-3 \); 11. Нет действительных решений; 12. Нет действительных решений.