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МатематикаРешить уравнения, обязательно помощью Дискриминанта.
Ответ:
Решение:
0,5x² = 0
\( \frac{1}{2}x^2 = 0 \)
\( x^2 = 0 \)
\( x = 0 \)
x² - 9 = 0
\( x^2 = 9 \)
\( x = \pm 3 \)
2x² + 15 = 0
\( 2x^2 = -15 \)
\( x^2 = -7.5 \)
Действительных корней нет.
x² - 12x + 36 = 0
\( D = b^2 - 4ac = (-12)^2 - 4 \cdot 1 \cdot 36 = 144 - 144 = 0 \)
\( x = \frac{-b}{2a} = \frac{12}{2} = 6 \)
3x² + 2x = 0
\( x(3x + 2) = 0 \)
\( x = 0 \) или \( 3x + 2 = 0 \)
\( x = -\frac{2}{3} \)
2x² - 16 = 0
\( 2x^2 = 16 \)
\( x^2 = 8 \)
\( x = \pm \sqrt{8} = \pm 2\sqrt{2} \)
5(x² + 2) = 2(x² + 5)
\( 5x^2 + 10 = 2x^2 + 10 \)
\( 3x^2 = 0 \)
\( x^2 = 0 \)
\( x = 0 \)
(x + 1)² - 4 = 0
\( (x + 1)^2 = 4 \)
\( x + 1 = \pm 2 \)
\( x = -1 \pm 2 \)
\( x_1 = -1 + 2 = 1 \)
\( x_2 = -1 - 2 = -3 \)
-1,5x² = 0
\( -\frac{3}{2}x^2 = 0 \)
\( x^2 = 0 \)
\( x = 0 \)
x² - 4 = 0
\( x^2 = 4 \)
\( x = \pm 2 \)
x² - 3x - 5 = 11 - 3x
\( x^2 - 3x - 5 - 11 + 3x = 0 \)
\( x^2 - 16 = 0 \)
\( x^2 = 16 \)
\( x = \pm 4 \)
5x² - 6 = 15x - 6
\( 5x^2 - 15x = 0 \)
\( 5x(x - 3) = 0 \)
\( x = 0 \) или \( x - 3 = 0 \)
\( x = 3 \)
x² + 2x - 3 = 2x + 6
\( x^2 + 2x - 3 - 2x - 6 = 0 \)
\( x^2 - 9 = 0 \)
\( x^2 = 9 \)
\( x = \pm 3 \)
2x² - 4x = x(6x - 3)
\( 2x^2 - 4x = 6x^2 - 3x \)
\( 0 = 6x^2 - 2x^2 - 3x + 4x \)
\( 0 = 4x^2 + x \)
\( x(4x + 1) = 0 \)
\( x = 0 \) или \( 4x + 1 = 0 \)
\( x = -\frac{1}{4} \)
Ответ: 1. x=0; 2. x=±3; 3. Действительных корней нет; 4. x=6; 5. x=0, x=-2/3; 6. x=±2√2; 7. x=0; 8. x=1, x=-3; 9. x=0; 10. x=±2; 11. x=±4; 12. x=0, x=3; 13. x=±3; 14. x=0, x=-1/4.
