Odpowiedź:
a)
[tex]\sqrt{7-4\sqrt{3} } +\sqrt{12+6\sqrt{3} }=\sqrt{4-4\sqrt{3}+3 }+\sqrt{9+6\sqrt{3} +3}=\\ =\sqrt{(2-\sqrt{3} )^{2} }+\sqrt{(3+\sqrt{3} )^{2} }=|2-\sqrt{3}|+|3+\sqrt{3}|=\\ =2-\sqrt{3}+3+\sqrt{3}=5=\frac{5}{1}[/tex]
b)
[tex]\sqrt{13+4\sqrt{3} }-\sqrt{21-12\sqrt{3} }=\sqrt{1+4\sqrt{3}+12 }-\sqrt{9-12\sqrt{3}+12}=\\ \sqrt{(1+2\sqrt{3} )^{2} } -\sqrt{(3-2\sqrt{3} )^{2} }=|1+2\sqrt{3}|-|3-2\sqrt{3} | =\\ 1+2\sqrt{3} -(-3+2\sqrt{3})=1+2\sqrt{3}+3-2\sqrt{3}=4=\frac{4}{1}[/tex]
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Odpowiedź:
a)
[tex]\sqrt{7-4\sqrt{3} } +\sqrt{12+6\sqrt{3} }=\sqrt{4-4\sqrt{3}+3 }+\sqrt{9+6\sqrt{3} +3}=\\ =\sqrt{(2-\sqrt{3} )^{2} }+\sqrt{(3+\sqrt{3} )^{2} }=|2-\sqrt{3}|+|3+\sqrt{3}|=\\ =2-\sqrt{3}+3+\sqrt{3}=5=\frac{5}{1}[/tex]
b)
[tex]\sqrt{13+4\sqrt{3} }-\sqrt{21-12\sqrt{3} }=\sqrt{1+4\sqrt{3}+12 }-\sqrt{9-12\sqrt{3}+12}=\\ \sqrt{(1+2\sqrt{3} )^{2} } -\sqrt{(3-2\sqrt{3} )^{2} }=|1+2\sqrt{3}|-|3-2\sqrt{3} | =\\ 1+2\sqrt{3} -(-3+2\sqrt{3})=1+2\sqrt{3}+3-2\sqrt{3}=4=\frac{4}{1}[/tex]