Question

Дам 30 баллов за решение

Answer 1

$1);5^8cdot2^6:10^7=5^8cdot2^6:(5^7cdot2^7)=5^{8-7}cdot2^{6-7}=5^1cdot2^{-1}=frac52=2frac12\2);frac{sqrt[3]3cdotsqrt[4]{4}}{sqrt[12]3}=3^{frac13}cdot4^{frac14}cdot3^{-frac1{12}}=3^{frac13-frac1{12}}cdot4^{frac14}=3^{frac14}cdot4^{frac14}=12^{frac14}=sqrt[4]{12}\3);frac{x^5cdot x^6}{x^9}=x^{5+6-9}=x^2=(12)^2=144\4);f(y)=(2y-frac3y)(3y-frac2y)=6y^2+frac6{y^2}-13\f(frac1y)=6cdotfrac1{y^2}+frac6{frac1{y^2}}-13=frac6{y^2}+6y^2-13\frac{f(y)}{f(frac1y)}=1$
$5);sin^235^o+sin^2125^o=frac{1-cos70^o}2+frac{1-cos250^o}2=frac{2-(cos70^o+cos250^o)}2=\=frac{2-2cos160^ocos90^o}2=frac{2-0}2=1\frac8{sin^235^o+sin^2125^o}=frac81=8\6);4cos2alpha=4cdot(2cos^2alpha-1)=4cdot(2cdotfrac1{16}-1)=4cdot(frac18-1)=\=4cdot(-frac78)=-frac74=-1frac34$