bai1: giai he phuong trinh: $\left\{ \begin{array}{l} x + y + \sqrt{x^{2}- y^{2}} = 12\\ y\sqrt{x^{2} - y^{2}} = 12 \end{array} \right.$
bai2: tim m de phuong trinh sau co nghiem: $\sqrt[4]{x^{2} + 1} - \sqrt{x} = m$

bai1:  cho E co phuong trinh:$ 3x^{2} + 5y^{2} = 30$
a/ tim toa do cac dinh, toa do cac tieu diem va tam sai cua elip
b/ 1 duong thang d qua tieu diem F2(2,0) cua E song song voi truc tung cat E tai 2 diem A va B. Tinh khoang cach tu A va B toi tieu diem F1

bai2: cho 2 Elip co phuong trinh: $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1 $ va $ \frac{x^{2}}{10} + y^{2} = 1$
chung minh rang 2 elip cat nhau tai 4 diem va 4 diem do cung nam tren 1 duong tron ma ta se viet duoc phuong tribnh

bai1: cho tam giac ABC co $\frac{c}{b} = \frac{m_{b}}{m_{c}} \neq 1$. chung minh rang
                 $\cot A = \frac{1}{2}(\cot B + \cot C)$

bai2: chung minh rang tam giac ABC deu neu thoa man 1 trong cac dieu kien sau:
a/ $\left\{ \begin{array}{l} \frac{b^{3} + c^{3} - a^{3}}{b + c - a} = a^{2}\\ a = 3b\cos C \end{array} \right.$
b/ $\left\{ \begin{array}{l} \frac{b^{3} + c^{3} - a^{3}}{b + c - a} = a^{2}\\ \frac{1}{\sin B} + \frac{1}{\sin C} = \frac{4}{\sin B + \sin C}\end{array} \right.$

chung minh rang neu A, B, C la 3 goc cua 1 tam giac ABC thi
a/ $\sin \frac{A + B + 3C}{2} = \cos C$
b/ $\cos ( A + B - C) = -\cos 2C$
c/ $\tan \frac{A + B - 2C}{2} = \cot \frac{3C}{2}$

bai 1: giai pt: $2x + 1 + x\sqrt{x^{2} + 2} + (x + 1)\sqrt{x^{2} + 2x + 3} = 0$

bai 2: giai pt:$ \sqrt[3]{x + 34} - \sqrt[3]{x - 3} = 1$