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МатематикаВопрос:
a) (2x - 3)(5x - 4) = 2x - 1\(\frac{3}{5}\);
Ответ:
a) $$(2x - 3)(5x - 4) = 2x - 1\frac{3}{5}$$;
$$(2x - 3)(5x - 4) = 2x - \frac{8}{5}$$;
$$10x^2 - 8x - 15x + 12 = 2x - \frac{8}{5}$$;
$$10x^2 - 23x + 12 - 2x + \frac{8}{5} = 0$$;
$$10x^2 - 25x + \frac{60+8}{5} = 0$$;
$$10x^2 - 25x + \frac{68}{5} = 0$$;
$$50x^2 - 125x + 68 = 0$$;
$$D = (-125)^2 - 4 \cdot 50 \cdot 68 = 15625 - 13600 = 2025$$;
$$x_1 = \frac{125 + 45}{100} = \frac{170}{100} = \frac{17}{10} = 1.7$$;
$$x_2 = \frac{125 - 45}{100} = \frac{80}{100} = \frac{8}{10} = 0.8$$;
Ответ: $$x = 1.7, x = 0.8$$
$$(2x - 3)(5x - 4) = 2x - \frac{8}{5}$$;
$$10x^2 - 8x - 15x + 12 = 2x - \frac{8}{5}$$;
$$10x^2 - 23x + 12 - 2x + \frac{8}{5} = 0$$;
$$10x^2 - 25x + \frac{60+8}{5} = 0$$;
$$10x^2 - 25x + \frac{68}{5} = 0$$;
$$50x^2 - 125x + 68 = 0$$;
$$D = (-125)^2 - 4 \cdot 50 \cdot 68 = 15625 - 13600 = 2025$$;
$$x_1 = \frac{125 + 45}{100} = \frac{170}{100} = \frac{17}{10} = 1.7$$;
$$x_2 = \frac{125 - 45}{100} = \frac{80}{100} = \frac{8}{10} = 0.8$$;
Ответ: $$x = 1.7, x = 0.8$$
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