Question

Помогите сделать 25. 26

Answer 1

$1); ; a=-sqrt6,; ; frac{a^3sqrt6}{12} = frac{-6sqrt6cdot sqrt6}{12} =-1\\2); ; x=sqrt{10}; ,; ; frac{250}{x^5sqrt{10}} = frac{250}{(sqrt{10})^5cdot sqrt{10}} = frac{250}{10^3} =frac{25}{100}=0,25\\3); ; m=frac{2}{3}; ,; ; n=frac{1}{2} ; ,\\frac{2n+3m}{6mn^2} - frac{9m-2n}{9m^2n} = frac{3m(2n+3m)-2n(9m-2n)}{18m^2n^2} = frac{-12mn+9m^2+4n^2}{18m^2n^2} =\\= frac{(3m-4n)^2}{18m^2n^2} = frac{(2-2)^2}{18cdot frac{1}{3}} =0$

$4); ; x=frac{1}{2}; ,; ; y=frac{1}{5}\\frac{12x+5y}{4x^2y} - frac{5y-4x}{5xy^2} = frac{5y(12x+5y)-4x(5y-4x)}{20x^2y^2} = frac{40xy+25y^2+16x^2}{20x^2y^2} =\\= frac{(4x+5y)^2}{20x^2y^2}= frac{(2+1)^2}{20cdot frac{1}{4}cdot frac{1}{25}} = frac{9cdot 25}{5}=9cdot 5=45$

$5); ; y=2x^2-8x-7\\x_{vershinu}=-frac{-8}{2cdot 2}=2\\y_{vershinu}=y(2)=8-16-7=-15$

Наименьшее значение функции = -15