Question

Помогите пожалуйста с квадратными уравнениями (даю 30 баллов)

Answer 1

#1.

$3x^2 + 6x = 0\\3x(x + 2) = 0\\3x = 0; x+2 = 0\\x = 0; x = -2$

#2.

$-2x^2 + 8x = 0\\-2x(x - 4) = 0\\\\\left[\begin{array}{cc}-2x = 0\\x - 4 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = 4\end{array}\right$

#3.

$x^2 - 4x = 0\\x (x - 4) = 0\\\\\left[\begin{array}{cc}x = 0\\x - 4 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = 4\end{array}\right$

#4.

$7x^2 - 14x = 0\\7x(x - 2) = 0\\\\\left[\begin{array}{cc}7x = 0\\x - 2 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = 2\end{array}\right$

#5.

$8x^2 + 3x = 0\\x(8x + 3) = 0\\\\\left[\begin{array}{cc}x = 0\\8x +3 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\8x = -3\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = \frac{-3}{8} \end{array}\right$

#6.

$-x^2 + 8x = 0\\-x(x - 8) = 0\\\left[\begin{array}{cc}-x = 0\\x -8 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = 8\end{array}\right$

#7.

a)

$x^2 + 1 = 82\\x^2 = 82 - 1\\x^2 = 81\\\\\left[\begin{array}{cc}x = 9\\x = -9\end{array}\right$

б)

$5x^2 = 20\\x^2 = 20 : 5\\x^2 = 4\\\\\left[\begin{array}{cc}x = 2\\x = -2\end{array}\right$

в)

$x^2 - 0,5x = 0\\x (x - 0,5) = 0\\\\\left[\begin{array}{cc}x = 0\\x -0,5 = 0\end{array}\right\\\\\left[\begin{array}{cc}x = 0\\x = 0,5\end{array}\right$