Question

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

Answer 1

• $x^2+y^2+8\geq4(x+y)\\x^2-4x+4\geq-y^2+4y-4\\(x-2)^2\geq-(y-2)^2\\\begin{array}{cc}(x-2)^2\geq0&(y-2)^2\geq0\\&-(y-2)^2\leq0\end{array}\\-(y-2)^2\leq0\leq(x-2)^2$

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

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

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

• $\begin{array}{cc}44^0\leq\alpha\leq45^0&72^0\leq\beta\leq73^0\end{array}\\\gamma=180^0-\alpha-\beta\\62^0\leq\gamma\leq64^0$

• $\begin{array}{cc}10.7\leq a\leq10.8&4.3\leq b\leq4.4\end{array}\\m=\frac{a+b}2\\7.5\leq m\leq7.6$