0,\; \to \; z<0\\\\64z^2=9(35+7z^2)\\\\z^2=315\\\\z=\pm \sqrt{315}=\pm 3\sqrt{35}\\\\Onvet:\; z=-3\sqrt{35}" alt="cos150^{\circ }=\frac{\overline {a}\cdot \overline {b}}{|\overline {a}|\cdot |\overline {b}|}\\\\-\frac{\sqrt3}{2}=\frac{-2+2+4z}{\sqrt{1+4+16}\cdot \sqrt{4+1+z^2}}\\\\\frac{4z}{\sqrt{21}\cdot \sqrt{5+z^2}}=-\frac{\sqrt3}{2}\\\\-8z=3\sqrt7\cdot \sqrt{5+z^2}\\\\-8z=3\sqrt{35+7z^2}\; \; \to \; \; -8z>0,\; \to \; z<0\\\\64z^2=9(35+7z^2)\\\\z^2=315\\\\z=\pm \sqrt{315}=\pm 3\sqrt{35}\\\\Onvet:\; z=-3\sqrt{35}" align="absmiddle" class="latex-formula">