Question

решите корни.
$\frac{5+3\sqrt{3} }{(\sqrt{3)} +2}$
$\frac{4}{(\sqrt{3)+1} }$

Answer 1

1)  $\frac{5+3\sqrt{3} }{(\sqrt{3} )+2} =\frac{(5+3\sqrt{3})*(\sqrt{3}-2) }{(\sqrt{3} +2)*(\sqrt{3}-2 )} =\frac{5\sqrt{3}+3*3-10-6\sqrt{3} }{(\sqrt{3} )^2-2^2} =\frac{-1-\sqrt{3} }{3-4} =\frac{-(1+\sqrt{3}) }{-1} =1+\sqrt{3}$

2)       $\frac{4}{\sqrt{3}+1}= \frac{4*(\sqrt{3}-1) }{(\sqrt{3}+1)*(\sqrt{3} +2)}= \frac{4*(\sqrt{3}-1) }{(\sqrt{3})^2-1^2}= \frac{4*(\sqrt{3}-1) }{3-1}=$

        $= \frac{4*(\sqrt{3}-1) }{2}=2*(\sqrt{3} -1)=2\sqrt{3} -2$