Question

Помогите сделать 25. 26

Answer 1

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

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

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

Наименьшее значение функции = -15