Question

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

Answer 1

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