Найдите сумму корней (или корень,если он единственный) уравнения [tex](( \int\limits'(

Найдите сумму корней (или корень,если он единственный) уравнения [tex](( \int\limits'( x))^{2} =4+ \frac{ \int\limits(-1)}{2+ x} [/tex] ,где [tex] \int\limits( x)=ln(2+ x)[/tex]
- Предмет:
  Математика
- Автор:
  elisha
- 6 лет назад

Ответы 1

$f(x)=ln(2+x)\\\\f'(x)=\frac{1}{2+x}\; ,\; \; (f'(x))^2=\frac{1}{(2+x)^2}\\\\f(-1)=ln(2-1)=ln1=0\\\\(f'(x))^2=4+\frac{f(-1)}{2+x}\; \; \to \; \; \frac{1}{(2+x)^2}=4+0\\\\(2+x)^2=\frac{1}{4}\\\\2+x=\pm \frac{1}{2}\\\\x= \frac{1}{2}-2=-1,5\; \; ili\; \; x=-\frac{1}{2}-2=-2,5\\\\Summa\; kornej\; =\; -4.$
- Автор:
  axelfjom
- 6 лет назад
- 0
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Найдите сумму корней (или корень,если он единственный) уравнения [tex](( \int\limits'( x))^{2} =4+ \frac{ \int\limits(-1)}{2+ x} [/tex] ,где [tex] \int\limits( x)=ln(2+ x)[/tex]

Ответы 1

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