Question

[Thảo Nguyễn]

Cho bieu thuc: P= \(\left(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}+\dfrac{3x-15}{9-x}\right):\dfrac{3}{\sqrt{x}+3}\)

a) Rut gon

b) Tinh gia tri cua P khi x=\(11-6\sqrt{2}\)

c) Voi x<9, tim gia tri lon nhat cua P

Bai 2: Cho nua duong tron tam O, duong kinh AB=2R. Tren cung nua mat phang bo AB dung 2 tiep tuyen Ax va By voi nua duong tron. Lay diem C thuoc nua duong tron, tiep tuyen tai C voi duong tron(O) cat Ax, By lan luot o M va N. Chung minh:

a) A,M,C,O cung thuoc mot duong tron O

b) Gia su AC cat By tai D. Chung minh: AC.AD=\(4R^2\)

c) AB la tiep tuyen cua duong tron duong kinh MN

d) Tim vi tri cua C tren duong tron de tong AM+BN co gia tri nho nhat

CAC BAN GIUM MINH VOI!! MINH DANG CAN GAP TRONG NGAY MAI NHE!! CAM ON CAC BAN NHIEU

Answer 1

[Nguyễn Lê Phước Thịnh]

Câu 1: 

a: \(P=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x+15}{x-9}\cdot\dfrac{\sqrt{x}+3}{3}\)

\(=\dfrac{-3\sqrt{x}+15}{\sqrt{x}-3}\cdot\dfrac{1}{3}=\dfrac{-\sqrt{x}+5}{\sqrt{x}-3}\)

b: Thay \(x=11-6\sqrt{2}\) vào P, ta được:

\(P=\dfrac{-\left(3-\sqrt{2}\right)+5}{3-\sqrt{2}-3}=\dfrac{-3+\sqrt{2}+5}{-\sqrt{2}}\)

\(=\dfrac{2-\sqrt{2}}{-\sqrt{2}}=-\sqrt{2}+1\)