Answer:
1)
[tex]12\sqrt{18}-3\sqrt{50}+\sqrt{32}[/tex]
[tex]12\sqrt{9}\sqrt{2}-3\sqrt{25} \sqrt{2} +\sqrt{16} \sqrt{2}[/tex]
[tex]12\times3\sqrt{2} -3\times5\sqrt{2}+4\sqrt{2}[/tex]
[tex]36\sqrt{2}-15\sqrt{2}+4\sqrt{2}[/tex]
[tex]25\sqrt{2}[/tex]
2)
[tex]\frac{1}{5+2\sqrt{6}}[/tex]
Multiply [tex]5-2\sqrt{6}[/tex]:
[tex]\frac{1\times \left(5-2\sqrt{6}\right)}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}[/tex]
Apply Difference of Squares formula: [tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]\frac{5-2\sqrt{6}}{5^2-\left(2\sqrt{6}\right)^2}[/tex]
[tex]\frac{5-2\sqrt{6}}{25-2^2\left(\sqrt{6}\right)^2}[/tex]
[tex]\frac{5-2\sqrt{6}}{25-4\times6}[/tex]
[tex]\frac{5-2\sqrt{6}}{1}[/tex]
[tex]{5-2\sqrt{6}}[/tex]
a = 5, b = -2
