Question

[Huỳnh Phương Khuê]

tìm m để pt 3sinx +m^2 - 2 =0 có nghiệm thuộc (-pi/3;pi/2)

Answer 1

[Loan]

=> \(\sin x=\frac{2-m^2}{3}\) (*)

khi \(x\in\left(\frac{-\pi}{3};\frac{\pi}{2}\right)\) => \(\sin x\in\left(\frac{-\sqrt{3}}{2};1\right)\)

Để (*) có nghiệm \(x\in\left(\frac{-\pi}{3};\frac{\pi}{2}\right)\) <=> \(\frac{2-m^2}{3}\in\left(\frac{-\sqrt{3}}{2};1\right)\)

<=> \(\frac{-\sqrt{3}}{2}\le\frac{2-m^2}{3}\le1\Leftrightarrow\frac{-3\sqrt{3}}{2}\le2-m^2\le3\Leftrightarrow\frac{-3\sqrt{3}-4}{2}\le-m^2\le1\)

<=> \(-1\le m^2\le\frac{4+3\sqrt{3}}{2}\Leftrightarrow-\sqrt{\frac{4+3\sqrt{3}}{2}}\le m\le\sqrt{\frac{4+3\sqrt{3}}{2}}\) 

Vậy với \(-\sqrt{\frac{4+3\sqrt{3}}{2}}\le m\le\sqrt{\frac{4+3\sqrt{3}}{2}}\) thì pt .....

Answer 2

[Đặng Trần Anh Thư]

C. Tây ban-nha, Bồ-đào-nha