Rút gọn :

B= \(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+1}+\frac{\sqrt{x}+8}{4-\sqrt{x}}\) ( x \(\ge\) 0 ; x \(\ne\)16)

Rút gọn :

A= \(\left(\frac{3\sqrt{2}-\sqrt{6}}{\sqrt{27}-3}-\frac{\sqrt{150}}{3}\right).\frac{1}{\sqrt{6}}\)

Cho f(x) = ax² + bx + 2018 và f(1+\(\sqrt{2}\) ) = 2019 . Xác định a , b

Rút gọn :

A=5.\(\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\frac{5}{2}}\right)^2\) + \(\left(\sqrt{2+\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\frac{3}{2}}\right)^2\)

Rút gọn :

a.C=(2-\(\sqrt{3}\) ) . \(\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right).\sqrt{26-15\sqrt{3}}\)

Cho a,b tm : \(\left\{{}\begin{matrix}\sqrt{a+5}+\sqrt{b-2}=3\\\sqrt{a-7}-4.\sqrt{b+1}=-6\end{matrix}\right.\) . Tính P= a-4b+2019

Cho x,y,z>0 tm : \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}+\sqrt{z}=2\\x+y+z=2\end{matrix}\right.\) .Tính:

P= \(\sqrt{\left(x+1\right).\left(y+1\right).\left(z+1\right)}.\left(\frac{\sqrt{x}}{x+1}+\frac{\sqrt{y}}{y+1}+\frac{\sqrt{z}}{z+1}\right)\)

Cho a= \(\frac{3+\sqrt{5}}{2}\) , b= \(\frac{3-\sqrt{5}}{2}\). Tính : P= \(\frac{1}{a^5}+\frac{1}{b^5}\)

Cho tam giác ABC cân tại A ( góc A < 90 độ).Đường cao AH.CM : \(\frac{AH}{CH}=2.\left(\frac{AB}{AC}\right)^2-1\)