Решите уравнение: (5x+2)^2-(3x+5)^2=0.

Ответ:

\[(5x + 2)^{2} - (3x + 5)^{2} = 0\]

\[25x^{2} + 20x + 4 - 9x^{2} - 30x - 25 = 0\]

\[16x^{2} - 10x - 21 = 0\]

\[D = 25 + 336 = 361 = 19^{2}\]

\[x_{1} = \frac{5 + 19}{16} = \frac{24}{16} = \frac{3}{2} = 1,5;\]

\[x_{2} = \frac{5 - 19}{16} = - \frac{14}{16} = - \frac{7}{8}.\]

\[Ответ:x = - \frac{7}{8};x = 1,5.\]