a, \(P=\frac{a}{\sqrt{a}-1}-\frac{2a-\sqrt{a}}{a-\sqrt{a}}=\frac{a}{\sqrt{a}-1}-\frac{2\sqrt{a}-1}{\sqrt{a}-1}\)với a > 0, a khác 1 

\(=\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}-1}=\sqrt{a}-1\)

TL:

vẫn = vô cực

-HT-

Đung thì mình kích 

\(\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)

\(=\sqrt[3]{\left(\sqrt{3}+1\right)^3}-\sqrt[3]{\left(\sqrt{3}-1\right)^3}\)

\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)=2\)

chỗ học ko để nói xàm xí ở đây

\(\sin75^o=\cos\left(90^o-75^o\right)=\cos15^o\)

\(\cos66^o=\sin\left(90^o-66^o\right)=\sin24^o\)

\(\tan47^o=\cot\left(90^o-47^o\right)=\cot43^o\)

\(\cot65^o=\tan\left(90^o-65^o\right)=\tan25^o\)

a/ \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

\(=\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(1+2\sqrt{2}\right)^2}\)

\(=3-2\sqrt{2}+1+2\sqrt{2}=4\)

b/ \(\sqrt{16+2\sqrt{63}}-\sqrt{16-6\sqrt{7}}\)

\(=\sqrt{\left(3+\sqrt{7}\right)^2}-\sqrt{\left(3-\sqrt{7}\right)^2}\)

\(=3+\sqrt{7}-3+\sqrt{7}=2\sqrt{7}\)

\(\sqrt{17-3\sqrt{32}}+\sqrt{17-3\sqrt{32}}\)

\(=\sqrt{17-3\sqrt{16.2}}+\sqrt{17-3\sqrt{16.2}}\)

\(=\sqrt{17-12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)

\(=\sqrt{9-2.3.2\sqrt{2}+8}+\sqrt{9-2.3.2\sqrt{2}+8}\)

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

\(=3-2\sqrt{2}+3-2\sqrt{2}\)

\(=6-4\sqrt{2}\)

\(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

\(=\sqrt{\left(4+2\sqrt{2}\right)^2}-\sqrt{\left(4-2\sqrt{2}\right)^2}\)

\(=4+2\sqrt{2}-4+2\sqrt{2}=4\sqrt{2}\)