Задание 3. Найдите корень уравнения. 1) (x-5)²=(x-8)²; 2) (x+9)2=(x+6)2; 3) (x+10)²=(5-x)²; 4) (x-3)2=(x+10)2; 5) (x+6)2=(15-x)²; 6) (x-2)2=(x-9)2. Задание 4. Найдите корень уравнения. 1) (x+1)2+(x-6)² = 2x²; 2) (x-2)²+(x-8)² = 2x²; 3) (x-6)²+(x+8)² = 2x²; 4) (x-2)²+(x-3)² = 2x2.

Задание 3

1. \[(x-5)^2 = (x-8)^2\] \[x^2 - 10x + 25 = x^2 - 16x + 64\] \[6x = 39\] \[x = \frac{39}{6} = \frac{13}{2} = 6.5\]

   Ответ: 6.5

2. \[(x+9)^2 = (x+6)^2\] \[x^2 + 18x + 81 = x^2 + 12x + 36\] \[6x = -45\] \[x = -\frac{45}{6} = -\frac{15}{2} = -7.5\]

   Ответ: -7.5

3. \[(x+10)^2 = (5-x)^2\] \[x^2 + 20x + 100 = 25 - 10x + x^2\] \[30x = -75\] \[x = -\frac{75}{30} = -\frac{5}{2} = -2.5\]

   Ответ: -2.5

4. \[(x-3)^2 = (x+10)^2\] \[x^2 - 6x + 9 = x^2 + 20x + 100\] \[-26x = 91\] \[x = -\frac{91}{26} = -\frac{7}{2} = -3.5\]

   Ответ: -3.5

5. \[(x+6)^2 = (15-x)^2\] \[x^2 + 12x + 36 = 225 - 30x + x^2\] \[42x = 189\] \[x = \frac{189}{42} = \frac{9}{2} = 4.5\]

   Ответ: 4.5

6. \[(x-2)^2 = (x-9)^2\] \[x^2 - 4x + 4 = x^2 - 18x + 81\] \[14x = 77\] \[x = \frac{77}{14} = \frac{11}{2} = 5.5\]

   Ответ: 5.5

Задание 4

1. \[(x+1)^2 + (x-6)^2 = 2x^2\] \[x^2 + 2x + 1 + x^2 - 12x + 36 = 2x^2\] \[2x^2 - 10x + 37 = 2x^2\] \[-10x = -37\] \[x = \frac{37}{10} = 3.7\]

   Ответ: 3.7

2. \[(x-2)^2 + (x-8)^2 = 2x^2\] \[x^2 - 4x + 4 + x^2 - 16x + 64 = 2x^2\] \[2x^2 - 20x + 68 = 2x^2\] \[-20x = -68\] \[x = \frac{68}{20} = \frac{17}{5} = 3.4\]

   Ответ: 3.4

3. \[(x-6)^2 + (x+8)^2 = 2x^2\] \[x^2 - 12x + 36 + x^2 + 16x + 64 = 2x^2\] \[2x^2 + 4x + 100 = 2x^2\] \[4x = -100\] \[x = -25\]

   Ответ: -25

4. \[(x-2)^2 + (x-3)^2 = 2x^2\] \[x^2 - 4x + 4 + x^2 - 6x + 9 = 2x^2\] \[2x^2 - 10x + 13 = 2x^2\] \[-10x = -13\] \[x = \frac{13}{10} = 1.3\]

   Ответ: 1.3