rút gọn biểu thức

T= \(\left(\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}+\frac{x-81}{\sqrt{x}+9}\right).\frac{\sqrt{x}+2}{\sqrt{x}+3}+\sqrt{x}\) với x ≥0

giải phương trình

a) \(\sqrt{2x^2-\sqrt{2}x+\frac{1}{4}}=\sqrt{2}x\)

b) \(\sqrt{4x+8}+\frac{1}{3}\sqrt{9x+18}=3\sqrt{\frac{x+2}{4}}+\sqrt{2}\)

Tính

\(\frac{1}{2}\sqrt{\left(\sqrt{3}-2\right)^2}-\sqrt{\frac{2}{3}}.\sqrt{2-\sqrt{3}}\)

a)\(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-\frac{6\sqrt{2}-4}{3-\sqrt{2}}\)

b)\(\sqrt{2-\sqrt{3}}-\sqrt{\frac{3}{2}}\)

c)\(\frac{\sqrt{30}-\sqrt{2}}{\sqrt{8-\sqrt{15}}}-\sqrt{8-\sqrt{49+8\sqrt{3}}}\)

d) \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

e)\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

f)\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)

g)\(\frac{\frac{\sqrt{2+\sqrt{3}}}{2}}{\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)