a: \(P=\dfrac{x-13}{\sqrt{x-9}-2}\)

\(=\dfrac{x-9-4}{\sqrt{x-9}-2}\)

\(=\dfrac{\left(\sqrt{x-9}-2\right)\left(\sqrt{x-9}+2\right)}{\sqrt{x-9}-2}=\sqrt{x-9}+2\)

b: \(\sqrt{x-9}>=0\forall x\) thỏa mãn ĐKXĐ

=>\(\sqrt{x-9}+2>=2\forall x\) thỏa mãn ĐKXĐ

=>P>=2 với mọi x thỏa mãn ĐKXĐ

Dấu '=' xảy ra khi x-9=0

=>x=9

\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)

\(=\sqrt{43+2\cdot\sqrt{450}}\)

\(=\sqrt{25+2\cdot5\cdot3\sqrt{2}+18}\)

\(=\sqrt{\left(5+3\sqrt{2}\right)^2}=5+3\sqrt{2}\)

   13⁵.17³.a⁹.(13.17².a³)

= 13⁵.17³.13.17².a⁹.a³

= (13⁵.13).(17³.17²).(a⁹.a³)

= 13⁶.17⁵.a¹²

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

 = \(\sqrt{13+30\sqrt{2+\sqrt{\left(1+2\sqrt{2}\right)^2}}}\)= \(\sqrt{13+30\sqrt{\left(1+\sqrt{2}\right)^2}}\)

= \(\sqrt{43\:+30\sqrt{2}}\) = \(\sqrt{(25+2×5×3\sqrt{2}+18}\) = \(5\:+3\sqrt{2}\)

17/13 ; 14/23 ; 3/4; 9/13; 9/23; 1/4

17/13= 17/13 ,  14/23= 14/23 ,  75/100=3/4  ,   9/13=9/13  ,  9/23=9/23   ,  15/60=5/12

75/100 =15/20    15/60 = 3/12    còn lại giữ nguyên nha

a)  − 3 4

b)  − 3 4

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)=\(\sqrt{13+30\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}\)

=\(\sqrt{13+30\sqrt{2+\sqrt{8}+1}}\)=\(\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)=\(\sqrt{13+30\sqrt{2}+30}\)

=\(\sqrt{43+30\sqrt{2}}\)=\(\sqrt{\left(5+3\sqrt{2}\right)^2}\)=\(5+3\sqrt{2}\)