Question

Неравенства по алгебре 20 баллов
Задания 1,2,3,4,5 - на фото

Answer 1

• $x^2+y^2+8geq4(x+y)\x^2-4x+4geq-y^2+4y-4\(x-2)^2geq-(y-2)^2\begin{array}{cc}(x-2)^2geq0&(y-2)^2geq0\&-(y-2)^2leq0end{array}\-(y-2)^2leq0leq(x-2)^2$

• $4x^2+10>12x\4x^2-12x+10>0\D=144-160=-16<0\4x^2+10>12x$

• $begin{array}{cc}1.2<x<2.4&1.5<y<2.7\6.6<3x+2y<12.6&0.33<0.5x-0.1y<1.05\9<5xy<32.4&frac{85}{108}<frac1x+frac1y<1.5end{array}$

• $begin{array}{cc}2.4<sqrt6<2.5&2.6<sqrt7<2.7end{array}\sqrt{28}-sqrt{42}=2sqrt7-sqrt6cdotsqrt7=sqrt7(2-sqrt6)\-1.04>sqrt7(2-sqrt6)>-1.35$

• $begin{array}{cc}44^0leqalphaleq45^0&72^0leqbetaleq73^0end{array}\gamma=180^0-alpha-beta\62^0leqgammaleq64^0$

• $begin{array}{cc}10.7leq aleq10.8&4.3leq bleq4.4end{array}\m=frac{a+b}2\7.5leq mleq7.6$