Докажите равенство (2корень из 2+3)/(3-2корень из 2)=17+12корень из 2.

\[\frac{2\sqrt{2} + 3}{3 - 2\sqrt{2}} = 17 + 12\sqrt{2}\]

\[\frac{\left( 2\sqrt{2} + 3 \right)\left( 2\sqrt{2} + 3 \right)}{\left( 3 - 2\sqrt{2} \right)\left( 2\sqrt{2} + 3 \right)} =\]

\[= \frac{\left( 2\sqrt{2} + 3 \right)^{2}}{9 - 8} =\]

\[= \frac{8 + 12\sqrt{2} + 9}{1} =\]

\[= 17 + 12\sqrt{2} \Longrightarrow ч.т.д.\]