Question

Exercitiul 3............

Answer 1

   
[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]