Question

Помогите 20 баллов !!!!!

Answer 1

$displaystyle frac{9x-y}{3x+x^{0.5}y^{0.5}} = frac{(3x^{0.5}-y^{0.5})(3x^{0.5}+y^{0.5})}{x^{0.5}(3x^{0.5}+y^{0.5})} = frac{3x^{0.5}-y^{0.5}}{x^{0.5}} = frac{3x- sqrt{xy} }{x}$

Если x=10 и y=576, то $displaystyle frac{3x- sqrt{xy} }{x} = dfrac{3cdot 10-sqrt{10cdot 576}}{10} = frac{30- sqrt{5760} }{10}$


$displaystyle frac{4x-y}{2x+x^{0.5}y^{0.5}} = frac{(2x^{0.5}-y^{0.5})(2x^{0.5}+y^{0.5})}{x^{0.5}(2x^{0.5}+y^{0.5})}= frac{2x^{0.5}-y^{0.5}}{x^{0.5}}= frac{2x- sqrt{xy} }{x}$

Если x=32 и y=81, то $displaystyle frac{2x- sqrt{xy} }{x} =frac{2cdot 32- sqrt{32cdot81} }{32} =2- frac{9cdot 4sqrt{2}}{32} =2- frac{9sqrt{2}}{8}$

Answer 2

B44.
$frac{9x-y}{3x+x^{0,5}*y^{0,5}} = frac{(3x^{0,5})^2-(y^{0,5})^2}{x^{0,5}(3x^{0,5}+y^{0,5})} = \ \ = frac{(3x^{0,5}-y^{0,5})*(3x^{0,5}+y^{0,5})}{x^{0,5}(3x^{0,5}+y^{0,5})} =frac{3x^{0,5}-y^{0,5}}{x^{0,5}} = \ \ =3 - frac{y^{0,5}}{x^{0,5}} =3- sqrt{ frac{y}{x} }$

x = 10; y = 576
$3- sqrt{ frac{y}{x} } =3- sqrt{frac{576}{10}} =3- frac{24}{ sqrt{10} } =3-2,4 sqrt{10}$

B45.
$frac{4x-y}{2x+x^{0,5}y^{0,5}} = frac{(2 sqrt{x} )^2-( sqrt{y} )^2}{2 (sqrt{x})^2 + sqrt{xy} } = \ \ =frac{(2 sqrt{x}- sqrt{y} )(2 sqrt{x}+ sqrt{y})}{sqrt{x}(2 sqrt{x} + sqrt{y} ) } =frac{2 sqrt{x}- sqrt{y}}{sqrt{x} } =2- sqrt{frac{y}{x}}$

x = 32;  y = 81
$2- sqrt{frac{y}{x}} =2- sqrt{frac{81}{32}} =2- frac{9}{4 sqrt{2} } =2- frac{9 sqrt{2} }{8} =2-1,125 sqrt{2}$