Question

Найдите значение выражения n^3-√2n^2/n^2-2 при n=2√2

Answer 1

$\frac{n^3- \sqrt{2}n^2 }{n^2-2} = \frac{n^2(n- \sqrt{2}) }{(n- \sqrt{2})(n+ \sqrt{2})}= \frac{n^2}{n+ \sqrt{2}} \\ \\ \frac{n^2}{n+ \sqrt{2}} = \frac{(2 \sqrt{2} )^2}{2 \sqrt{2} + \sqrt{2} } =\frac{8}{3 \sqrt{2} }=\frac{4 \sqrt{2} }{3 }$