Question

Exercițiul 10
b; c; d;
Vă rog!!

Answer 1

$\displaystyle b)~\Big|2-\sqrt{5}\Big|-\Big|\sqrt{3}+\sqrt{5}\Big|+\Big|1-\sqrt{3}\Big|-\Big|\sqrt{3}-3\Big|=\\ \\ =\sqrt{5}-2-(\sqrt{5} +\sqrt{3} )+\sqrt{3} -1-(3-\sqrt{3} )=\\ \\ =\sqrt{5} -2-\sqrt{5} -\sqrt{3} +\sqrt{3} -1-3+\sqrt{3} =\mathbf{\sqrt{3} -6}$

$\displaystyle c)~\Big|\sqrt{3}+\sqrt{2}\Big|-\Big|\sqrt{3}+5\Big|-\Big|1-\sqrt{2}\Big|+\big|-5\big|=\\ \\ =\sqrt{3}+\sqrt{2}-(5+\sqrt{3})-(\sqrt{2}-1)+5=\\ \\=\sqrt{3}+\sqrt{2}-5-\sqrt{3}-\sqrt{2}+1+5=\mathbf{1}$

$\displaystyle d)~\Big|\sqrt{2}-\sqrt{3}\Big|+\Big|2-\sqrt{3}\Big|+\Big|1-\sqrt{2}\Big|-|-3|=\\ \\ =\sqrt{3}-\sqrt{2}+2-\sqrt{3}+\sqrt{2}-1-3=\mathbf{-2}$