Question

100 баллов! срочно! доказать тождество
$3 - \sqrt{8} = \frac{1}{3 + 2 \sqrt{2} }$
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Answer 1

Ответ:

$3-\sqrt{8} =\dfrac{1}{3+2\sqrt{2} }$

$\sqrt{8} =2\sqrt{2} \\3\sqrt{8} =3-2\sqrt{2}$

$\dfrac{1}{3+2\sqrt{2} } =\dfrac{1*(3-2\sqrt{2} )}{(3+2\sqrt{2})(3-2\sqrt{2} ) } =1*(3-2\sqrt{2} )=3-2\sqrt{2} =\dfrac{3-2\sqrt{2} }{1} =3-2\sqrt{2}$

$3-2\sqrt{2} =3-2\sqrt{2}$

Тожество доказано