1) Cho tam giac ABC nhon. 2 Duong cao AD va BE cat nhau tai H ( D ∈ BC, E ∈ AC)

a) Goi I la tam cua duong tron ngoai tiep tu giac CDHE. C/m IE la tiep tuyen cua duong tron duong kinh AB ( Ve hinh nua)

1) Cho bieu thuc \(A=\frac{x}{x-4}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)

a) Tim tat ca cac gia tri cua x de A>1

1) Goi x1,x2 la nghiem cua phuong trinh \(x^2-3x+2=0\)

a) Tinh tong S=x1+x2 va tich P= x1.x2

1) Cho \(R_1=R_2=R_3=R_4=R\) noi nhu hinh ve . Tinh \(R_{td}\) theo R ( bo qua dien tro cac day noi)

a)

1) Cho \(R_1=R_2=R_3=R_4=R\) noi nhu hinh ve. Tinh \(R_{tuongduong}\) theo R ( bo qua dien tro cac day noi)

a)

1) tim m de pt \(x^2-2\left(m+1\right)x+6m-4=0\)co 2 nghiem x1;x2 thoa man \(\left(2m-2\right)x_1+x_2^2-4x_2=4\)

1) Cho \(x\ge1,y\ge1\). Chung minh:

a) \(x\sqrt{y-1}+y\sqrt{x-1}\le xy\)

1) Cho x,y,z>0. Chung minh:

a) \(\frac{x^2}{x^2+2yz}+\frac{y^2}{y^2+2xz}+\frac{z^2}{z^2+2xy}\ge1\)

1) cho a,b,c,d > 0. C/m: \(\sqrt{\frac{a}{b+c+d}}+\sqrt{\frac{b}{c+d+a}}\sqrt{\frac{c}{d+a+b}}+\sqrt{\frac{d}{a+b+c}}>2\)

1) giai phuong trinh:

a) \(x+\sqrt{2x+3}=2x\left(x-2\right)\)