Question

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(Алгебра 10 класс)

Answer 1

$3*frac{sqrt{8+2sqrt7}}{sqrt{8-2sqrt7}}-frac{sqrt{3+sqrt7}}{sqrt{3-sqrt7}}*sqrt2=\ =3*frac{sqrt{1+2sqrt7+(sqrt7)^2}}{sqrt{1-2sqrt7+(sqrt7)^2}}-frac{sqrt{3+sqrt7}*sqrt{3+sqrt7}}{sqrt{3+sqrt7}*sqrt{3-sqrt7}}*sqrt2=\ =3*frac{sqrt{(1+sqrt7)^2}}{sqrt{(1-sqrt7)^2}}-frac{sqrt{(3+sqrt7)^2}}{sqrt{3^2-(sqrt7)^2}}*sqrt2=$
$=3*frac{1+sqrt7}{1-sqrt7}}-frac{3+sqrt7}{sqrt{9-7}}*sqrt2=\ =3*frac{(1+sqrt7)*(1+sqrt7)}{(1-sqrt7)*(1+sqrt7)}}-frac{3+sqrt7}{sqrt{2}}*sqrt2=\ =3*frac{(1+sqrt7)^2}{1-(sqrt7)^2}-3+sqrt7=3*frac{(1+sqrt7)^2}{1-7}-3+sqrt7=\ =3*frac{1+2sqrt7+7}{-6}-3+sqrt7=-frac{1+2sqrt7+7}{-2}-3+sqrt7=\ =frac{1+2sqrt7+7+6-2sqrt7}{-2}=frac{14}{-2}=-7$