Question

Упростите одно выражение

Answer 1

$left(sqrt[4]x+3sqrt[4]yright)^2-6sqrt[8]{x^5y^7}:sqrt[8]{x^3y^5}=\\=left(left(sqrt[4]xright)^2+2sqrt[4]{x}cdot3sqrt[4]{y}+left(3sqrt[4]yright)^2right)-frac{6sqrt[8]{x^5y^7}}{sqrt[8]{x^3y^5}}=\\=sqrt x+6sqrt[4]{xy}+9sqrt y-6 sqrt[8]{frac{x^5y^7}{x^3y^5}}=\\=sqrt x+6sqrt[4]{xy}+9sqrt y-6 sqrt[8]{x^{5-3}cdot y^{7-5}}=\\=sqrt x+6sqrt[4]{xy}+9sqrt y-6 sqrt[8]{x^{2}y^{2}}=sqrt x+6sqrt[4]{xy}+9sqrt y-6 sqrt[8]{left(xyright)^2}=$

$=sqrt x+6sqrt[4]{xy}+9sqrt y-6 sqrt[4]{xy}=sqrt x+9sqrt y.$