[tex]\displaystyle\\
a\Big(3\sqrt{3}-2\Big)+b\Big(4\sqrt{3}+1\Big)=26\sqrt{3}+1\\\\
3a\sqrt{3}-2a + 4b\sqrt{3}+b=26\sqrt{3}+1\\\\
\text{Separam numerele rationale de cele irationale si obtinem doua ecuatii.}\\\\
\left \{ {{3a\sqrt{3} + 4b\sqrt{3}=26\sqrt{3}~~~\Big|: \sqrt{3}}\atop {-2a +b=1}~~~~~~~~~~~~~~~~~~~~} \right. \\\\
\left \{ {{3a + 4b=26~~~~~~~~}\atop {-2a +b=1}~~~\Big|\cdot(-4)} \right.
[/tex]
[tex]\displaystyle\\
\left \{ {{3a + 4b=26}\atop {8a -4b=-4}} \right. \\
\text{- - - - - - - - - - - - adunam ecuatiile.}\\
~~~11a ~~/~~= 22\\\\
a = \frac{22}{11} =\boxed{2}\\\\
-2a +b=1\\\\
-2 \times 2 + b = 1\\
b = 1+2 \times 2= 1+4 = \boxed{5}[/tex]
