12* a) [tex] \sqrt{6} x^{2} = \sqrt{54} /: \sqrt{6} \\ x^{2} = 3 \\ x= \sqrt{3} [/tex]
b) [tex]6( x^{2} + \sqrt{3})= \sqrt{108} \\ 6 x^{2} +6 \sqrt{3}= \sqrt{108}/-6 \sqrt{3} \\ 6 x^{2} = 0/:6 \\ x^{2} =0=\ \textgreater \ x=0[/tex]
c) [tex](x+ \sqrt{3})(x- \sqrt{3})= 24 \\ \\ x^{2} -x \sqrt{3} +x\sqrt{3} -3=24 \\ \\ x^{2} -3=24/+3 \\ \\ x^{2} =27=\ \textgreater \ x=3 \sqrt{3}[/tex]
d) [tex] \frac{x^{2}} {\sqrt{11}-\sqrt{7}} =\sqrt{11}+\sqrt{7}/*\sqrt{11}-\sqrt{7} \\ \\ x^{2}=11-\sqrt{77}+\sqrt{77}-7 \\ \\ x^2=4=\ \textgreater \ x=2[/tex]
e) [tex](x- \sqrt{6})^{2}=24 \\ \\ x- \sqrt{6}=2\sqrt{6}/+\sqrt{6} \\ \\ x=3\sqrt{6}[/tex]
