giai he phuong trinh\(\left\{{}\begin{matrix}x^2+y^2-xy=19\\x+y+xy=-7\end{matrix}\right.\)

cho bieu thuc A=\(\left(\dfrac{6x+4}{3\sqrt{3x^3}-8}-\dfrac{\sqrt{3x}}{3x+2\sqrt{3x}+4}\right)\left(\dfrac{1+3\sqrt{3x^3}}{1+\sqrt{3x}}-\sqrt{3x}\right)\)

a.rut gon bieu thuc A

b. tim cac gia tri nguyen x de A nguyen

giai phuong trinh\(\dfrac{1}{x^2+4x+3}+\dfrac{1}{x^2+8x+15}+\dfrac{1}{x^2+12x+35}+\dfrac{1}{x^2+16x+63}=\dfrac{1}{5}\)

cho a,b,c>0va a+b+c=1 cm \(b+c\ge16abc\)

giai pt \(x^2+\left(\dfrac{x}{x+1}\right)^2=1\)

giai he phuongtrinh \(\left\{{}\begin{matrix}x^2+\dfrac{1}{y^2}+\dfrac{x}{y}=3\\x+\dfrac{1}{y}+\dfrac{x}{y}=3\end{matrix}\right.\)

cho x>0,y>0va x+y=1 cm \(8\left(x^4+y^4\right)+\dfrac{1}{xy}\ge5\)

giai pt\(\dfrac{x^2}{\left(\sqrt{x+1}+1\right)^2}=x-4\)

anh nang mat troi vao buoi trua chieu vao cay bang la phep chieu gi

tu giac ABCD noi tiep duong tron (O;R)co hai duong cheo AB,CD vuong goc voi nhau tai I (I khac O ). ve duong kinh CE.

a.chung minh ABDE la hinh thang can

b. chung minh \(\sqrt{AB^2+CD^2+BC^2+DA^2}=2R\sqrt{2}\)