1. 5x² - 5 = 0
5 ( x²-1) = 0
x² - 1 = 0
x² = 1
x = 1, x = -1
2. 12x² - 4 = 0
4 (3x² - 1) = 0
3x² - 1 = 0
x² = 1/3
x = 1/√3, x = -1/√3
3. 16 - 2x² = 0
2 (8 - x²) = 0
8 - x² = 0
x² = 8
x = √8 = 2√2, x = -2√2
4. -3x² = 9
x² = -3
квадрат какого-либо числа не может быть отрицательным, значит, корней у этого уравнения нет.
5. x² = 2,5
x = √2,5
x = -√2,5
6. 6x² - 9 = 15
6x² - 9 - 15 = 0
6x² - 24 = 0
6 (x² - 4) = 0
x² - 4 = 0
x² = 4
x = 2, x = -2
7. 3x² - 4x = 5 + 2x² - 4x
3x² - 4x - 2x² + 4x = 5
x² = 5
x = √5, x = -√5
8. 5x² - 14 + 8x = 8x
5x² + 8x - 8x = 14
5x²=14
x² = 14/5
x² = 2,8
x = √2,8
x = -√2,8
9. 8x² - 6x = -2(3x - 3)
8x² - 6x = -6x + 6
8x² - 6x + 6x = 6
8x² = 6
4x² = 3
x² = 3/4
x² = 0,75
x = √0,75
x = -√0,75
10. x² + 15(x - 2) = 3(5x + 1)
x² + 15x - 30 = 15x + 3
x² + 15x - 15x = 30 + 3
x² = 33
x = √33, x = -√33