Сколько решений имеет уравнение arcsin2x+arcsinx=П/3?

Сколько решений имеет уравнение arcsin2x+arcsinx=П/3?
- Предмет:
  Математика
- Автор:
  blossomoelk
- 5 лет назад

Ответы 1

Возьмем с каждой части $sin$ $sin(arcsin2x+arcsinx)=sin(\frac{\pi}{3})\\\\$ откуда $x\sqrt{1-4x^2}+2x\sqrt{1-x^2}=\frac{\sqrt{3}}{2}$ по формуле $sin( \alpha + \beta )$ . $x\sqrt{1-4x^2}+2x\sqrt{1-x^2}=\frac{\sqrt{3}}{2}\\$ рассмотреть функцию слева , он возрастает на $(0 ; \infty)$ , следовательно она имеет одно решение
- Автор:
  redkrueger
- 5 лет назад
- 0
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Сколько решений имеет уравнение arcsin2x+arcsinx=П/3?

Ответы 1

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