Question

40PCTE
Niciodata nu am inteles cum se fac astea si acum dau test din ele, HELP:

Aratati ca urmatoarele numere sunt rationale

a) $\sqrt{6-4\sqrt{2}} + \sqrt{6+4 \sqrt{2}}$
b) $\sqrt{12-6 \sqrt{3} } + \sqrt{12+6 \sqrt{3} }$

Answer 1

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Answer 2

a) =[tex] \sqrt{4- 4\sqrt{2}+2 }+ \sqrt{4+4 \sqrt{2}+2 }= \sqrt{(2- \sqrt{2})^2 }+ \sqrt{(2+ \sqrt{2})^2 }= [/tex]
$|2- \sqrt{2} |+|2+ \sqrt{2} |=2- \sqrt{2}+2+ \sqrt{2} =4$

b) $= \sqrt{9-6 \sqrt{3}+3 } + \sqrt{9+6 \sqrt{3}+3 }= \sqrt{(3- \sqrt{3})^2 } + \sqrt{(3+ \sqrt{3})^2 =$
$|3- \sqrt{3} |+|3+ \sqrt{3} |=3- \sqrt{3}+3+ \sqrt{3} =6$