Объяснение:

) 3x² - 15 = 0

3x² = 15

x² = 5

x₁ = - √ 5 x₂ = √5

2) 4x² - 7x = 0

x(4x - 7) = 0

или x₁ = 0 или 4x - 7 = 0

4x = 7

x₂ = 1,75

3) x² + 8x - 9 = 0

По теореме Виета : x₁ + x₂ = - 8 x₁ *x₂ = - 9 , значит

x₁ = - 9 x₂ = 1

4) 12x² - 5x - 2 = 0

D = (- 5)² - 4 * 12 * (- 2) = 25 + 96 = 121 = 11²

\begin{gathered}x_{1}=\frac{5+11}{24}=\frac{16}{24}=\frac{2}{3}\\\\x_{2}=\frac{5-11}{24}=-\frac{6}{24}=-0,25\end{gathered}

x

1

=

24

5+11

=

24

16

=

3

2

x

2

=

24

5−11

=−

24

6

=−0,25

5) x² - 6x - 3 = 0

D = (- 6)² - 4 * (- 3) = 36 + 12 = 48 = (4√3)²

\begin{gathered}x_{1}=\frac{6-4\sqrt{3}}{2}=3-2\sqrt{3}\\\\x_{2}=\frac{6+4\sqrt{3} }{2}=3+2\sqrt{3}\end{gathered}

x

1

=

2

6−4

3

=3−2

3

x

2

=

2

6+4

3

=3+2

3

6) x² - 3x + 11 = 0

D = (- 3)² - 4 * 11 = 9 - 44 < 0

Извини, но решений нет.