Question

aduceti la forma cea mai simpla....
va rog ajutatima....

Answer 1

a) $=( \sqrt{10- \sqrt{19} }) ^{2} + ( \sqrt{10+ \sqrt{19} } )^{2} +2 \sqrt{(10- \sqrt{19})*(10+ \sqrt{19}) }$=
$=10- \sqrt{19} +20+ \sqrt{19} +2 \sqrt{100-19} =$
$=20+2 \sqrt{81} =$
=20+2*9=38
b) $= ( \sqrt{2 \sqrt{5} +4}) ^{2} + ( \sqrt{2 \sqrt{5}-4 } )^{2} -2 \sqrt{(2 \sqrt{5} +4)*(2 \sqrt{5} -4)} =$
$=2 \sqrt{5}+4+2\sqrt{5}-4-2\sqrt{20-16}=$
$=4\sqrt{5}-2\sqrt{4}=$
$=4\sqrt{5}-4$

Answer 2

a)      
$(\sqrt{10 -\sqrt{19}}+\sqrt{10 + \sqrt{19}})^{2} = \\ = 10 -\sqrt{19} + 2\sqrt{10 -\sqrt{19}}*\sqrt{10 + \sqrt{19}} + 10 + \sqrt{19}= \\ =10 + 10 + 2 \sqrt{(10 -\sqrt{19})(10 + \sqrt{19})}= \\ =20 + 2 \sqrt{10^{2} -(\sqrt{19})^{2}}= \\ =20+2\sqrt{100 -19}= \\ =20+2 \sqrt{81}= \\ = 20 + 2*9 = \\ =20+18= \\ =38$


b)
$( \sqrt{2 \sqrt{5}+4}-\sqrt{2 \sqrt{5}-4})^{2}= \\ =(2\sqrt{5}+4)-2( \sqrt{2 \sqrt{5}+4}*\sqrt{2 \sqrt{5}-4}) + (2 \sqrt{5}-4})= \\ = 2\sqrt{5}+4 + 2\sqrt{5}-4 -2 \sqrt{(2\sqrt{5}+4)*(2\sqrt{5}-4)}= \\ =4\sqrt{5} - 2 \sqrt{(2\sqrt{5})^{2}-(4)^{2}}= \\ =4\sqrt{5} - 2 \sqrt{20-16}= \\ =4\sqrt{5}-2\sqrt{4}= \\ =4\sqrt{5}-2*2= \\ =4\sqrt{5}-4= \\ =4( \sqrt{5}-1)$