Question

помогите решить пожалуйста тему не поняла

Answer 1

$1); ; frac{sqrt5-sqrt3}{sqrt5+sqrt3} +frac{sqrt5+sqrt3}{sqrt5-sqrt3} = frac{(sqrt5-sqrt3)^2+(sqrt5+sqrt3)^2}{(sqrt5+sqrt3)(sqrt5-sqrt3)} =\\=frac{(5-2sqrt{15}+3)+(5+2sqrt{15}+3)}{5-3} =frac{16}{2} =8\\2)quad frac{1}{11-2sqrt{30}} - frac{1}{11+2sqrt{30}} = frac{11+2sqrt{30}-11+2sqrt{30}}{(11-2sqrt{30})(11+2sqrt{30})} =\\= frac{4sqrt{30}}{121-4cdot 30} = frac{4sqrt{30}}{121-120} =4sqrt{30}$

$3)quad frac{11+sqrt{21}}{11-sqrt{21}} + frac{11-sqrt{21}}{11+sqrt{21}}=frac{(11+sqrt{21})^2+(11-sqrt{21})^2}{(11+sqrt{21})(11-sqrt{21})}=\\= frac{(32+22sqrt{21})+(32-22sqrt{21})}{11^2-21}=frac{64}{121-21}=frac{64}{100} =0,64$

$4)quad frac{5}{3+2sqrt2} + frac{5}{3-2sqrt2} = frac{5(3-2sqrt2)+5(3+2sqrt2)}{3^2-4cdot 2} = frac{30}{9-8} =30$

$5)quad (3sqrt5+sqrt{15})^2-10sqrt{27}=9cdot 5+6sqrt{5cdot 15}+15-10sqrt{3cdot 9}=\\=45+15+6sqrt{5cdot 5cdot 3}-10cdot 3sqrt3=60+6cdot 5sqrt3-30sqrt3=\\=60+30sqrt3-30sqrt3=60$

Answer 2

спасибо большое!!!

Answer 3

Ещё один пример добавила.

Answer 4

я так благодарна вам,спасибо большое еще раз