Question

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Answer 1

$\it 9) \ \ -3<-2,5<-2 \Rightarrow [2,5]=-3\\ \\ -\sqrt{36}<-\sqrt{27}<-\sqrt{25} \Rightarrow -6<-\sqrt{27}<-5 \Rightarrow [-\sqrt{27}]=-6\\ \\ Expresia\ \ din\ \ enun\c{\it t}\ \ devine:\\ \\ -3-(-6)=-3+6=3$

$\it 8)\ A=\{x\in\mathbb{R}\Big|\sqrt{(2x+3)^2}\leq9\}\\ \\ \sqrt{(2x+3)^2}\leq9 \Rightarrow |2x+3|\leq9 \Rightarrow -9\leq2x+3\leq9|_{-3} \Rightarrow\\ \\ \Rightarrow -12\leq2x\leq6|_{:2} \Rightarrow -6\leq x\leq3 \Rightarrow A=[-6,\ \ 3]$

$\it 7)\ \ [a;\ b)\cap\mathbb{Z}=\{-3,\ \ -2\} \Rightarrow \{-3,\ \ -2\}\subset[a;\ \ b) \Rightarrow a=-3,\ \ b=-1$

$\it 6)\ \ -2\sqrt3=-\sqrt{2^2\cdot3}=-\sqrt{12}\\ \\ -3\sqrt2=-\sqrt{3^2\cdot2}=-\sqrt{18}\\ \\ -\sqrt{18}<-\sqrt{12} \Rightarrow -3\sqrt2<-2\sqrt3$